I think accidents are oft-times the best because of the spontaneous nature to them. We don't pay that much attention to composition or lighting or anything. And sometimes, the accidental photos wind up better in terms of both composition and lighting. I went to Germany last year and when I got bored, I'd just go out and take photos completely at random. And one of my favourite photos I made was of this windmill in Xanten:
I didn't plan it at all. Literally just pointed and shot. Same with this one, taken not fifty feet down the road:
This following one was more of a pure accident as I forgot to turn on the flash. Three of my friends and I (still in Germany) were out on the patio of a bar and we were a bit drunk:
Maybe it's just me, but I like this one a lot. And the blurriness gives the photo an added inebriation effect.