We leave the door open a small amount - I like to be able to peek in and check on her without it creaking as it opens! As for the fire thing - yes, closed doors keep the fire from spreading, but if a fire starts, we have smoke detectors, and the plan is to get the kid out, not leave them in there as the fire burns, so I don't see how that's an issue - we could alway close the door as we flee the house. As for wandering around - we have a gate at the top of the stairs, and that would be the only risk. Plus, for some reason, DD won't leave her bed once she's put in for the night - the very first night in her big bed, she walked out and we (firmly) told her to go back to bed, and she's never left on her own since!
I suppose if there was lots of noise in the house, we'd close the door, but I know I grew up sleeping with the door open and it was less scary than feeling closed in all alone in my room...