Do you mean no mouse at all, as in no cursor, or are we allowed to suggest games that can be played easily with a mouse substitute such as a touch-pad or nipple (yes that's a real term!)?
If it's the former you're pretty much stuck with flash games, some racing games might be possible too. If you can get some form of cursor control then flight sims become possible and RTSs can easily be played with a touch-pad or ball mouse. You'll never be the very fastest at an RTS without using a good mouse, but you should be able to get good enough to beat the computer or friends & family members.
Running emulators of old consol titles might also be possible, though bear in mind that depending on the game and your country this may not be legal.