TypeRacer - Enter a name and click "Accept" to start racing! Then type the quote from a well-known movie, book or song as fast as you can. You must be 100% accurate! Loads of fun.
Keybr.com - Just a basic keyboard practice session. Use the mouse to click on the word "Pause" and start typing what's at the top of the screen. For an empty box, hit the space bar.
TyperShark – Type words and letters to keep your diver alive. Good (and challenging) for all levels. Tip: Don’t use your space bar or the Enter key!
Gamequarium: Keyboarding – This site also offers both lessons and games, although even the lessons here can be fun. (They are created for kids, though, so don’t expect maturity.)
Ninja Hunter - If traditional video games are your thing, you'll probably enjoy this one from Addicting Games, where the words you type keep ninjas at bay. Let enough past and you'll have to fight!
Most of these sites require you to register; registration will allow you to keep track of your progress and pick up where you left off.
Quick tip: There are many more free typing games and tutorials available online, and you can find them with a simple Google search. If you are asked to pick a keyboard, you want the QWERTY keyboard, U.S. version.