RPGs: Traps. I prefer running a sword through my enemies.
Old-school FPSes: Rocket launchers or any other "BFG." I hoard them for hard enemies, then I forget about them and beat the game with the regular guns anyway.
Newer FPSes: Any weapon that has a long reload time. I'm a compulsive reloader, so these weapons often spell doom for me.
Racing games: Vehicles with good speed, but terrible handling. I prefer taking turns and corners easily over going fast on straight stretches.