Just a few I can think of, but some may need a gaming mouse to get all the controls mapped:
Audiosurf 1 + 2
Crayon Physics Deluxe
Diablo 1, 2 & 3
Dragon Age Origins & Dragon Age 2
Fallout 1, 2 & Tactics
Guild Wars 2
Legend of Grimrock
Monkey Island series
Poker Night at the Inventory & Poker Night 2
Plants vs Zombies
Puzzle Quest series
Revenge of the Titans
Sam & Max series
Torchlight 1 & 2
World of Goo
Genres like click-adventures are a safe bet. I was going to suggest The Walking Dead Telltale games but I believe the quick time events are mapped to the keyboard and no option to remap. Someone can correct me if I'm wrong.
Puzzle, tower defense and sport management games rarely need more than a mouse to control them. If none of the above suggestions take your fancy take a look at the Steam categories and you'll find something which does I'm sure
If you want to read more about the accessibility of some I mentioned, Able Gamers is a great source for reviews.
Will post later if I remember more.
Magic The Gathering series
These are technically in the RTS genre but more "city-builder" rather than something like StarCraft 2 etc:
Cities in Motion
Rollercoaster Tycoon series.