Late in the game, as usual.

Spinner: right hand, unless right hand is using a joystick (dotron, forgotten worlds).
Trackball: Well, depends on the game. Usually the right hand, except some games without buttons (marble madness) or times in games that the buttons aren't used, and the trackball needs to
move I use both (you know, quickly alternating hands). Also, I find if I need to move right or right down quickly, I switch to my left hand a lot of the time, and don't bother to switch back to my right hand if there are buttons on both sides. I switch back if I need to move left or left down quickly, or maybe at a break.