If you're interested in a game that involves both speed and typing, Typing Bowl is a fun multiplayer game where you race against other online players to type a quote as fast and accurately as possible.
I didn't think I'd enjoy this game as much as I did, but I ended up playing at least 10 rounds. To play, simply click "join race," and when a new race starts, you'll be paired against a group of other players. The races start every 5 seconds or so.
The game gives everyone the same quote, and you have to type it out, making sure to include proper spacing and punctuation. The letters in the quote turn either blue or red as you type (depending on the accuracy), so you know where you are in the game. Besides being totally addictive to play, I like that this game has an educational purpose and actually helps me improve my typing.