I'd suspect that the crack is caused by movement of the exterior walls of your house up and down a little bit. That could be due to frost heave or the clay in the soil around your house swelling (due to lotsa moisture) or shrinking (due to it drying out).
I'm thinking that the reason why the crack is forming there is that the corner of a doorway is the weakest spot in an interior wall. Think of the doorway as a big notch in a wall spanning across the house. If the wall has to bend, and the plaster or drywall has to crack to accomodate that movement, it'll crack at the weakest spot, which is at the top corners of any doorways through that wall.
If the crack is due to up and down movement of the foundation (and hence exterior walls), then the movement will persist until you find out what's causing it. If you want to fix this crack in the mean time, what I would do is apply joint compound to the crack (just with my fingers) and then wipe the area on each side of the crack down with a damp sponge to remove the excess joint compound. Allow the joint compound along the crack line to dry, and then wipe across the crack line with a damp sponge to remove any excess joint compound in the crack line.
Now prime and paint with a matching colour paint using an artist's paint brush or a maybe a 3 inch roller sleeve.