Good Controller Based Games

Dark Souls, unplayed? Time to fix this mistake.
Ys Origin and Sonic CD are good choices too.

I find 3rd person games play well on controls: Dark Souls, GTA4, Batman, Fable.
Platformers too: Mark of the Ninja, Sonic etc

Mark of the Ninja and Psychonauts demand to be played.

Mark of the ninja

Batman works well on controller, as does Witcher 2 (you'll may need to remap the radial menu, you do for the SHIELD but may be fine with a 'normal' controller).

Red Faction Armageddon is another good controller game, features a enemy 'lock on' button which is a handy compensation for the lack of fidelity you have by not using a mouse.

Batman, Mark of the Ninja, Rogue Legacy, Dark Souls, Super Meat Boy, Dead Space, The Binding of Isaac, The Walking Dead, most indie titles.

you can also use this program called joytokey to play games without a crontoller option like the binding of isaac

Risk of rain,
Spelunky,
Rogue legacy,
Binding of isaac (with a controller emulator),
unepic,
skullgirls.

Suuuuper MEAT BOY!

Bastion, Batman, DARKSOULS!! (try this game without controller), Portal2 are games I played with controller. Great games :)

Anything that is also on console.