Using a holo-emitter, the Doctor can travel anywhere.  Without it, he can only exist in the holodeck and sickbay.  There are distinct benefits to being a hologram.  The Doctor can modulate his magnetic containment field to allow matter to pass through it or be stopped (basically things can pass through him, like he was a ghost, or he can be solid like a person), which has advantages.  He can walk through containment fields.  The Doctor is often immune to situations that render the rest of the crew helpless.  The Captain once turned over the command codes to the Doctor for that reason.

He is often irritable, and it used to be said he had a lousy bedside manner.  The crew has come to accept him, although in the beginning he was often insulted and ignored.  The Doctor has a dry sense of humor.  He has tried to give himself personalites from famous people, but failed and became an evil hologram.  Luckily, B'Elanna fixed the problem, and now he is without those personalities.