Marble Madness. Any game with a trackball, really.
Arkanoid. The NES controller that came with that version was ok, but the game was different enough that it wasn't the same for me. Any game with a spinner is different.
APB. Not the new MMO, but the old-school, top-down cop driving game. I have it on the Lynx, and it's not the same without a steering wheel and pedals.
And as a bonus... one I wouldn't want to re-create at home.
Street Fighter. The first one, with the pressure sensitive buttons. Hitting the button harder for tougher attacks? Wacky!