The two current leading theories waffle between the Roman Emperor Nero and Mrs. O'Leary's cow.

No one did. It was always burning, since the world's been turning. That indicates it predates life.

I'm not a historian, but all I've ever read or heard it that we didn't start it. Maybe someone else will come in with a more solid answer but I doubt it.

We didn't start the fire.

I guess this prompts a similar question: When did the world start turning?

I believe Dr. Schrute once concluded that Ryan started the fire.

The world is turning on a kebab-spit. The fire is what's cooking it. Whoever started the fire has been preparing the world to be eaten since it's been turning. That's why global warming is happening -- because we're literally getting cooked.