Wizard of Wor. (Technically uses 9-way sticks, but no one has those (4-way sticks with 2 levels of sensitivity on each direction).
The entire Mr. Driller series (not yet in Mame).
Tetris (most versions).
Bloxeed.
A lot of other puzzle games.
And Uo Poko is actually an 8-way game, not 4-way like was previously thought, as you can roll the joystick around the circle back to up in order to let the chain back up again.