When do you pick a genre? Or how?

I had a moment of insight as I was reading through other blogs. When I begin writing something, I usually start with a first sentence and see where my fingers take me. Its a flaw really, because I don't outline anything (something I've noticed as a problem I need to fix) and worlds just begin to exist within my mind. Sometime down the road, I'm a thousand words into a project and people are born, conflicts built, realities now existing where they didn't before. I don't really figure out where I'm going with things though until I'm well into it.

About the second chapter (maybe) or so, I start to decide a general direction and then I'm off, like a jackrabbit running from the fox. The fox is my right on my heels, and the finish line I'm searching for is two words: The End. I'm usually hopping along so fast though - building paths as I go - that I have no idea what type of world it is I'm running in. Add to that the fact that I'm not entirely clear on figuring out what type of world it should be anyway. Categorization has never really been my forte, and learning how to do it with my writing has been agonizing. So the question I pose is when do you pick a genre? Is it after you've already gotten the premise of the story down? Or do you find yourself beginning a thriller only to find its actually romance? Do your characters start out YA and become literary? I don't really have answers for myself here, but I'm open to anyone else's thoughts.