This depends on what you're trying to say. "On the airplane" implies that something is literally on the outside of the airplane, such as the logo, paint, or something sitting on the wings. "In the...
George Carlin had a bit on this. "I'm getting IN the plane! In the plane! Let Evil Kneivel get ON the plane. I'll be in here with you folks in uniform. There seems to be less wind in here."