Twicca - Twicca is a Twitter client for Android that is simply awesome. Features: * Notification
TweetDeck - TweetDeck is your personal browser for staying in touch with what’s happening now.
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.
Twitterfall - Twitterfall is an excellent choice if you want something basic, free and without much branding.
Tweedle App - Notion is nice but sometimes all you need is an app like Tweedle.
Tweetdeckr - Tweetdeckr is an open source Tweetdeck replacement client.