Suggest a game that can be played without a mouse.

Super mario, pacman.

Binding of Isaac

VVVVVV
Cave Story+

those learn to type games that toddlers play.

Sims. Oh wait, that's ONLY mouse. Get some old space invaders ripoff for free or something, I'm sure it won't need a mouse.

limbo

Doom 2 is super cute --- lol

Any game on emulator imo :D (or console game, no one told it has to be a steam or pc game :D) We had a blast playing Super Smash Bros with my friends.

Fortix!

Perhaps some adult game, you don't need mouse nor second hand.

Jamestown

Altitude, LIMBO, Nightsky, Nimbus

Limboooooooooo

Get some SNES or GBA games. I personally recommend Terranigma and Illusion of Time for the SNES, for GBA, Pokemon, Golden Sun, Megaman Zero. For PC, get DMC 3: Dante's Awakening SE

AudioSurf

both bittrip games

How is Limbo cute? XD
I'd say Blocks That Matter. Excellent game.

The Binding Of Isaac, Chance Of Replay: 95%

Tetris

The Touhou Games are great!

Suuuuuper Meat Boy, but if you use a joypad is better.

Every game that can be played on controller? Unless you don't have one or something...

TITANS ATTACK!~

BINDING OF ISAAC!

BLOCKS THAT MATTER!

Grand Theft Auto (Not just the top-down ones) can actually be played without a mouse, using the Num Pad to control the camera. Lots of games will work without a mouse as long as you have a Num Pad to control the camera :) (Although trying to rebind keys could be hard, unless the game allows you to navigate with arrow keys or WASD.... just activate Mouse Keys then, under the Sticky Keys options. Quickly tap that shift button and use Tab + Num Pad to navigate!)

Also, Worms.

Limbo, Braid, Super Meat Boy, Rayman (all of them), and any racing game should be playable without a mouse.