It may not have as much functionality as Tweetie, but does your Twitter app let you jump through a tweet timeline like you're playing a Mario platformer? For $2, you're getting a Twitter client and Game Center-enabled game.
Running in a similar landscape format as Plurk and iStreamer, the tweets glide by horizontally in the Super Twario world, where you can create tweets, reply and retweet. Everything you do inside the app lets you rack up and unlock scores and achievements, which are transferred to Game Center.
Controls including tapping to jump, swiping to run faster, and using the accelerometer you can tilt the iPhone to guide your playable character Twario through the various tweets if you want to actually, you know, read them.