Tweetbot - Sync your timeline across your iPhone, iPad, and Mac. Mute tweets by user, hashtag, tweet source, or keywords (including regex). 3rd Party support for image, video, read later, and timeline sync services.
TweetDeck - TweetDeck is your personal browser for staying in touch with what’s happening now.
Twitterrific - Twitterific is an app that offers several functions and fun features for your Twitter account.
Twitterfall - Twitterfall is an excellent choice if you want something basic, free and without much branding.
X (Twitter) - Connect with your friends and other fascinating people. Get in-the-moment updates on the things that interest you. And watch events unfold, in real time, from every angle.
Tweetdeckr - Tweetdeckr is an open source Tweetdeck replacement client.