Tying Strings

Man, I still blog, right? I think I had some feeling there was more to write about my last post, but I couldn't come up with anything so I just put it off. Now it seems apparent that that one is just plain done so its time to move on to something more interesting. So, new puzzle, I first learned this one on the forums at xkcd:

You have a bowl of N strings, each the same length. A string is a line segment with two indistinguishable ends, and all the strings are indistinguishable. You randomly select two ends of the strings from the bowl (they might be on the same string, they might not) and tie them together (fuse them, if you prefer). You repeat this process until there are no more ends left and you just have loops of string. On average, how many loops of string do you have?

There are other questions you can ask in this scenario, but to save myself blogging material I'll hold onto them for later.