SuperTuxCart is a free 3D kart racing game.
The authors say the game is more about fun than realism, and that's plain from the selection of tracks: you can race underground, or in space, for instance, while opponents try to put you off by throwing bowling balls, bubble gum and cakes, amongst other objects.
The physics of the karts are quite realistic, though, so they're quite easy to drive. The program should recognise most game controllers and joysticks right away, but if not you can always use the keyboard, which defaults to the standard driving controls (arrow keys to steer, brake and accelerate, space to fire and so on).
And you can then keep yourself entertained by racing on more than 20 tracks, and with multiple game modes. So you can simply do time trials on your own to improve your lap times; run single races against other computer-controlled carts; compete in various Grand Prix; battle your friends in a split-screen multiplayer mode, and more.
Note that this is the portable version of SuperTuxCart.