How many times has the white house caught on fire?

Twice ... Yes it was burned by the British in the war of 1812. The story goes that Dolly Madison was running out the door with the painting of Washington as the British troops entered. That is the reason why the house it white. The paint was used to paint over the burn marks and when they did some work on the White House they found some of the burn marks from 1812.

On Christmas Eve 1929 the White House experienced its most powerful fire since the British torched the Executive Mansion 115 years earlier.