I've literally had problems; I've been ready to tear my hair out over, which have been answered in the time I spent going to fetch another cup of coffee.
This alone makes this site worth it for me. Yes, I spend a few minutes now and then answering questions, but I consider that investing into the site in such a way that it helps survive and be there tomorrow when I need it again. I think many feel the same way.
Note that this is both entirely selfish and some sort of help-your-fellow-programmer type of thing.
I love helping people, and I think that counts for some part of my addiction to Stack Overflow. I was a member of the IRC Delphi community a while back for a number of years and most of the time it was just plain fun helping people.
But the biggest reason is entirely selfish. I want Stack Overflow to be there when I have my hair-tearing-out problems, and I want the maximum number of eyeballs to look over my oddball question and really give me shot-in-the-dark answers, if for no other reason than confirming my beliefs that this is indeed an oddball problem.
And I think this is sort of the goal of the site as well. Attract a good sized number of people who wants more than just a drive-by range of questions and answers, you want a community, where people build on others knowledge and the circle just goes around and around.
I think Stack Overflow has really proved its worth already. It might not be known to everyone, but that'll happen fast. Jeff Atwood already mentions, frequently on their podcast, that around 80% of their traffic comes from Google.
And to me that doesn't really matter. The site has already proven its weight in gold (or time, time is more precious than gold these days), so for me it's just an investment.
And a good one I might add.