UPDATE: Tweetie is now the Official Twitter App for iPhone, simply called Twitter
The app so nice he made it Twice! Tweetie 2 is an award-winning Twitter app for the iPhone and iPod Touch, stowing away an unbelievable number of features into a simple, easy, attractive interface. Seriously!! Every pixel of this interface is precisely designed and intuitive to use.
TweetDeck is an Adobe AIR Twitter app for power users. Using a column layout, TweetDeck allows a user to set up many feeds at once. Some are specialized to Twitter, such as your friends, @ mentions, direct messages and so forth. But the real power lies in their numerous advanced search features, which filter the public timeline any way you desire: