See also a book Tom has referenced from time to time; vollentary fraternal mutual aid associations at one time did exist – even though all the current “market failure/collective action problem” models say they couldn’t have.
If these organizations did an imperfect job, 1) society as a whole was a lot poorer then; we could do much better now and 2) it is not as if the welfare state model, either here or in the U.S., is actually more effective at getting people out of poverty (quite the contrary in fact. Indeed there have been a recent flurry of statistics showing how it entraps people). The welfare state model is also, necessarily, “one-size-fits all” policy, while private mutual aid & charitable organizations can tailor things to the recipient. A still-existing example is: what’s the most effective and prominent institution that helps addicts in need of help? It’s not a government program, it’s AA.
This is an old problem; Bastiat once wrote that “every time we object to a thing being done by government, the socialists conclude that we object to its being done at all” – a problem that extends beyond self-described socialists to…well, practically everyone, nowdays. Partly because people have confused ‘society’ with “state” – they’ll ask “don’t you want to live in a society where X?” (X being: the poor are helped, or health care is available to those who need it, and so on), and but then they either imply or directly assert that means the state does it.
(I’ve concluded that, as an intellectual/philosophical problem, the origin of this failure to distinguish between society and state lays with social contract theory. Thus it is necessary for libertarians to make sure people understand the distinction between the two and keep it in mind at all times, because it’s all too easy in a society founded on the basis of classical liberal social contract theory to lose sight of this distinction).
There are a couple other sources like the Beito book that Tom has mentioned, but they slip my mind now, which address how people were helped, and how they helped themselves, in the time before the welfare state crowded most of these institutions – the institutions of true civil society – out.* Hopefully he’ll post and mention some of them. A lot of these arguments for private provision of aid are in his book Rollback, which I recommend highly.
*Not all of them disappeared, but some were utterly transformed; for example, the Bank of America was originally founded to help Italian immigrants. It still exist, of course, but now it’s just another member of the banking system.