Developer Firemint (makers of the extremely popular Flight Control and Real Racing games) is about to release its latest game Spy Mouse. Along with parent company EA, it's hosting a contest to let a few players into the game early. You have to log in with Twitter over on this page, then "answer the clue," a new one every day, to be entered to win. You can also do a little social networking promotion for Firemint to increase your chances. For every 100 likes the company gets on its Facebook page, another winner will get picked for the current clue.
In addition to playing the game early, Firemint's also giving away copies of EA games like Dead Space and The Sims 3. If you're interested to see what Firemint's been up to as early as possible (and for free), definitely give the contest a look. Heck, you could always do what I do: Send the promotional tweets out on a completely separate Twitter account, which lets you get the word out there without bothering your usual followers.