The concept of "social capital" is slippery to measure or analyze, but the OECD, for example, defines it as “networks together with shared norms, values and understandings that facilitate co-operation within or among groups.” The great economist Kenneth Arrow wrote in a 1972 essay on "Gifts and Exchanges" (Philosophy & Public Affairs, 1:4 (Summer 1972), pp. 343-362): 
"Many of us consider it possible that the process of exchange requires or at least is greatly facilitated by the presence of several of these virtues (not only truth, but also trust, loyalty, and justice in future dealings). Now virtue may not always be its own reward, but in any case it is not usually bought and paid for at market rates. In short, the supply of a commodity in many respects complementary to those usually thought of as economic goods is not itself accomplished in the marketplace ... Virtually every commercial transaction has within itself an element of trust, certainly any transaction conducted over a period of time. It can be plausibly argued that much of the economic backwardness in the world can be explained by the lack of mutual confidence ... "
Any discussion of American networks soon starts quoting the French writer Alexis de Tocqueville,who noted an oddity about Americans in his classic Democracy in America (published in two volumes in 1835 and 1840): Americans had a predilection what he called associations. He wrote:
"Americans of all ages, all conditions, and all dispositions, constantly form associations. They have not only commercial and manufacturing companies, in which all take part, but associations of a thousand other kinds—religious, moral, serious, futile, extensive, or restricted, enormous or diminutive. The Americans make associations to give entertainments, to found establishments for education, to build inns, to construct churches, to diffuse books, to send missionaries to the antipodes; and in this manner they found hospitals, prisons, and schools. ... Nothing, in my opinion, is more deserving of our attention than the intellectual and moral associations of America. The political and industrial associations of that country strike us forcibly; but the others elude our observation, or if we discover them, we understand them imperfectly, because we have hardly ever seen anything of the kind. It must, however, be acknowledged that they are as necessary to the American people as the former, and perhaps more so. In democratic countries the science of association is the mother of science; the progress of all the rest depends upon the progress it has made."  
But while the idea that social capital is important is far from new, it's nonetheless interesting that the staff of the Joint Economic Committee of Congress has just published a report "What We Do Together: The State of Associational Life in America  (Social Capital Project Report 01-17, May 2017). It's studded with quotations from authors like Tocqueville and Robert "Bowling Alone" Putnam.

Before listing some facts about changes in what the report calls "associational life" in America, it's perhaps useful for me to confess that while I can easily believe that social capital is generally important, the specific processes by which it is created and reinforced are not clear to me. It would be peculiar and anachronistic to yearn after the good old days of 1840. If the people of 1840 had radio, television, and the internet, not to mention the ability to hop in a car or a plane and travel, then the "associations" observed by Tocqueville would have looked rather different. The question of what social institutions are most useful to inculcate the growth of a citizens with a predisposition to cooperation and trust is a vast ocean, and I am just a guy in dinghy, padding around with one small oar.

In other words, I think it's important and useful to think about how associational life is shifting: that is, who we rely on, who relies on us, and how we interact with other citizens in a variety of cross-cutting forums. It does feel as if we are, along a number of dimensions, living in a lower-trust time. But whether or how to address these changes is beyond my remit. Here are some of the patterns mentioned in the Congressional report, which include associations related to family, religion, community, politics, and work.  For those with a taste for Tocqueville, I'll include some additional context from Democracy and America below:

Some changes in family associations

  •  Between 1973 and 2016, the percentage of Americans age 18-64 who lived with a relative declined from 92 percent to 79 percent. The decline was driven by a dramatic 21-point drop in the percentage who were living with a spouse, from 71 percent to 50 percent.
  • In 1970, there were 76.5 marriages per 1,000 unmarried women aged 15 and older. As of 2015, that rate had declined by more than half to 32 per thousand. 
  • In 1970, 56 percent of American families included at least one child, but by 2016 just 42 percent did. The average family with children had 2.3 children in 1970 but just 1.9 in 2016. Among all families—with or without children—the average number of children per family has dropped from 1.3 to 0.8. 

Some changes in religious associations

  • In the early 1970s, nearly seven in ten adults in America were still members of a church or synagogue. While fewer Americans attended religious service regularly, 50 to 57 percent did so at least once per month. Today, just 55 percent of adults are members of a church or synagogue, while just 42 to 44 percent attend religious service at least monthly. 
  • In the early 1970s, 98 percent of adults had been raised in a religion, and just 5 percent reported no religious preference. Today, however, the share of adults who report having been raised in a religion is down to 91 percent, and 18 to 22 percent of adults report no religious preference. 

Some changes in community associations

  • Between 1974 and 2016, the percent of adults who said they spend a social evening with a neighbor at least several times a week fell from 30 percent to 19 percent.
  • Between 1970 and the early 2010s, the share of families in large metropolitan areas who lived in middle-income neighborhoods declined from 65 percent to 40 percent. Over that same time period the share of families living in poor neighborhoods rose from 19 percent to 30 percent, and those living in affluent neighborhoods rose from 17 percent to 30 percent.
  • Between 1972 and 2016, the share of adults who thought most people could be trusted declined from 46 percent to 31 percent. Between 1974 and 2016, the number of Americans expressing a great deal or fair amount of trust in the judgement of the American people “under our democratic system about the issues facing our country” fell from 83 percent to 56 percent.
  • Between 1974 and 2015, the share of adults that did any volunteering who reported volunteering for at least 100 hours increased from 28 percent to 34 percent.

Some changes in political associations
• Between 1972 and 2012, the share of the voting-age population that was registered to vote fell from 72 percent to 65 percent, and the trend was similar for the nonpresidential election years of 1974 and 2014. Correspondingly, between 1972 and 2012, voting rates fell from 63 percent to 57 percent (and fell from 1974 to 2014).
• Between 1972 and 2008, the share of people saying they follow “what’s going on in government and public affairs” declined from 36 percent to 26 percent.
• Between 1972 and 2012, the share of Americans who tried to persuade someone else to vote a particular way increased from 32 percent to 40 percent.
Some changes in work associations
 • Between the mid-1970s and 2012, the average amount of time Americans between the ages of 25 and 54 spent with their coworkers outside the workplace fell from about two-and-a-half hours to just under one hour.
• Work has become rarer, in particular, among men with less education. From the mid-1970s to 2012, hours at work fell by just 2 percent among men with a college degree or an advanced degree, compared with 14 percent among those with no more than a high school education.
• Between 1995 and 2015, workers in “alternative work arrangements” (e.g., temp jobs, independent contracting, etc.) grew from 9 percent to 16 percent of the workforce.
• Since 2004, median job tenure has been higher than its 1973 level, indicating that workers are staying in their jobs longer than in the past.
• Between 1970 and 2015, union membership declined from about 27 percent to 11 percent of all wage and salary workers.
For those who need a larger dose of Tocqueville, here's a more extended quotation from his discussion of Americans and "associations" in Book II, Chapters 5-7 of Democracy in America 
(the Project Gutenberg edition). Toward the end of the excerpt, in particular, Tocqueville argues that freedom of association in political, civic, and economic interactions is all intertwined: when people learn how to form associations, it spreads across these varied contexts.
"The political associations which exist in the United States are only a single feature in the midst of the immense assemblage of associations in that country. Americans of all ages, all conditions, and all dispositions, constantly form associations. They have not only commercial and manufacturing companies, in which all take part, but associations of a thousand other kinds—religious, moral, serious, futile, extensive, or restricted, enormous or diminutive. The Americans make associations to give entertainments, to found establishments for education, to build inns, to construct churches, to diffuse books, to send missionaries to the antipodes; and in this manner they found hospitals, prisons, and schools. If it be proposed to advance some truth, or to foster some feeling by the encouragement of a great example, they form a society. Wherever, at the head of some new undertaking, you see the government in France, or a man of rank in England, in the United States you will be sure to find an association. ... The English often perform great things singly; whereas the Americans form associations for the smallest undertakings. It is evident that the former people consider association as a powerful means of action, but the latter seem to regard it as the only means they have of acting. ...
Aristocratic communities always contain, amongst a multitude of persons who by themselves are powerless, a small number of powerful and wealthy citizens, each of whom can achieve great undertakings single-handed. In aristocratic societies men do not need to combine in order to act, because they are strongly held together. Every wealthy and powerful citizen constitutes the head of a permanent and compulsory association, composed of all those who are dependent upon him, or whom he makes subservient to the execution of his designs. Amongst democratic nations, on the contrary, all the citizens are independent and feeble; they can do hardly anything by themselves, and none of them can oblige his fellow-men to lend him their assistance. They all, therefore, fall into a state of incapacity, if they do not learn voluntarily to help each other. If men living in democratic countries had no right and no inclination to associate for political purposes, their independence would be in great jeopardy; but they might long preserve their wealth and their cultivation: whereas if they never acquired the habit of forming associations in ordinary life, civilization itself would be endangered. ... 
As soon as several of the inhabitants of the United States have taken up an opinion or a feeling which they wish to promote in the world, they look out for mutual assistance; and as soon as they have found each other out, they combine. From that moment they are no longer isolated men, but a power seen from afar, whose actions serve for an example, and whose language is listened to. The first time I heard in the United States that 100,000 men had bound themselves publicly to abstain from spirituous liquors, it appeared to me more like a joke than a serious engagement; and I did not at once perceive why these temperate citizens could not content themselves with drinking water by their own firesides. I at last understood that 300,000 Americans, alarmed by the progress of drunkenness around them, had made up their minds to patronize temperance. ...
Nothing, in my opinion, is more deserving of our attention than the intellectual and moral associations of America. The political and industrial associations of that country strike us forcibly; but the others elude our observation, or if we discover them, we understand them imperfectly, because we have hardly ever seen anything of the kind. It must, however, be acknowledged that they are as necessary to the American people as the former, and perhaps more so. In democratic countries the science of association is the mother of science; the progress of all the rest depends upon the progress it has made. ...
In order that an association amongst a democratic people should have any power, it must be a numerous body. The persons of whom it is composed are therefore scattered over a wide extent, and each of them is detained in the place of his domicile by the narrowness of his income, or by the small unremitting exertions by which he earns it. Means then must be found to converse every day without seeing each other, and to take steps in common without having met. Thus hardly any democratic association can do without newspapers. There is consequently a necessary connection between public associations and newspapers: newspapers make associations, and associations make newspapers; and if it has been correctly advanced that associations will increase in number as the conditions of men become more equal, it is not less certain that the number of newspapers increases in proportion to that of associations. Thus it is in America that we find at the same time the greatest number of associations and of newspapers. ...

There is only one country on the face of the earth where the citizens enjoy unlimited freedom of association for political purposes. This same country is the only one in the world where the continual exercise of the right of association has been introduced into civil life, and where all the advantages which civilization can confer are procured by means of it. ...  Civil associations, therefore, facilitate political association: but, on the other hand, political association singularly strengthens and improves associations for civil purposes. In civil life every man may, strictly speaking, fancy that he can provide for his own wants; in politics, he can fancy no such thing. When a people, then, have any knowledge of public life, the notion of association, and the wish to coalesce, present themselves every day to the minds of the whole community: whatever natural repugnance may restrain men from acting in concert, they will always be ready to combine for the sake of a party. Thus political life makes the love and practice of association more general; it imparts a desire of union, and teaches the means of combination to numbers of men who would have always lived apart. ... 
Men can embark in few civil partnerships without risking a portion of their possessions; this is the case with all manufacturing and trading companies. When men are as yet but little versed in the art of association, and are unacquainted with its principal rules, they are afraid, when first they combine in this manner, of buying their experience dear. They therefore prefer depriving themselves of a powerful instrument of success to running the risks which attend the use of it. They are, however, less reluctant to join political associations, which appear to them to be without danger, because they adventure no money in them. But they cannot belong to these associations for any length of time without finding out how order is maintained amongst a large number of men, and by what contrivance they are made to advance, harmoniously and methodically, to the same object. Thus they learn to surrender their own will to that of all the rest, and to make their own exertions subordinate to the common impulse—things which it is not less necessary to know in civil than in political associations. Political associations may therefore be considered as large free schools, where all the members of the community go to learn the general theory of association. ...
It is therefore chimerical to suppose that the spirit of association, when it is repressed on some one point, will nevertheless display the same vigor on all others; and that if men be allowed to prosecute certain undertakings in common, that is quite enough for them eagerly to set about them. When the members of a community are allowed and accustomed to combine for all purposes, they will combine as readily for the lesser as for the more important ones; but if they are only allowed to combine for small affairs, they will be neither inclined nor able to effect it. It is in vain that you will leave them entirely free to prosecute their business on joint-stock account: they will hardly care to avail themselves of the rights you have granted to them; and, after having exhausted your strength in vain efforts to put down prohibited associations, you will be surprised that you cannot persuade men to form the associations you encourage. ... 
When you see the Americans freely and constantly forming associations for the purpose of promoting some political principle, of raising one man to the head of affairs, or of wresting power from another, you have some difficulty in understanding that men so independent do not constantly fall into the abuse of freedom. If, on the other hand, you survey the infinite number of trading companies which are in operation in the United States, and perceive that the Americans are on every side unceasingly engaged in the execution of important and difficult plans, which the slightest revolution would throw into confusion, you will readily comprehend why people so well employed are by no means tempted to perturb the State, nor to destroy that public tranquillity by which they all profit. ... 
Is it enough to observe these things separately, or should we not discover the hidden tie which connects them? In their political associations, the Americans of all conditions, minds, and ages, daily acquire a general taste for association, and grow accustomed to the use of it. There they meet together in large numbers, they converse, they listen to each other, and they are mutually stimulated to all sorts of undertakings. They afterwards transfer to civil life the notions they have thus acquired, and make them subservient to a thousand purposes. Thus it is by the enjoyment of a dangerous freedom that the Americans learn the art of rendering the dangers of freedom less formidable.