i would bet that you may have a whacked front end which may need realignment. have you hit any deep potholes lately?
your test of pulling to the right may be influenced by the crown in the road. try finding a road that is flat, or as tester suggested a parking lot.
i would suggest an interstate highway which has the camber in the center lane, so you can go from the left lane, (which is usually cambered to the left) then go to the right lane (which is usually cambered to the right). see if either lane makes a difference as to how much it pulls (more or less).
does this only happen when you brake? or is it anytime? is it worse when you brake? does the crown of the road make it better or worse (depending which side of the crown you are on?)