I close both of my doors. Habit from having pets, I don't like them to jump on the bed while I am sleeping. The last dog I had wanted to be crated at night, but I still had a cat that roamed around at night. It also blocks out all of the ambient light from the other rooms.
One door leads to the hallway and the other bedrooms, and my library... and the other door is my private door to the theater/media room.
Oh, I even close my bathroom door. I have a skylight and love to sleep in total darkness!