Everyone (including us) seems to be creating fun gadgets and mash-ups using Twitter’s API.  Here is a list from the unofficial Twitter wiki:

• BBC News - Get BBC news headlines via twitter. Main news feed, and individual news channels available.
• EgorCast Now you can call in your Twitter posts. EgorCast is a mashup of Jott.com/Twitter/Jaiku.
• TweeTweeT! Now you can Twitter while watching live public Tweets as a cartoon. Finally.
• Twitterment is a Twitter search engine that also provides trend graphs and identifies buzzy and fading terms.
• MoniTwitter Monitors your website, posting updates to Twitter about load times and whether there is a problem or not. Subscribe to the Twitter account to receive updates about your site, notifications if it goes down.
• Twitterverse - a mashup and visualization project by Ideacodes which mines and archives the public timeline of Twitter and provides a visualization of the most commonly used words in a given time period.
• ServerMojo - free server monitoring system now with server status alerts sent via Twitter!
• Twitter Atlas - The twitter public timeline viewed in Atlas by Fresh Logic Studios updated every 5 seconds.
• twittermap - See current updates from Twitter users in a specific local area, and update your location in realtime by specifying L:21012 (or L: + any geocodable location) in a Twitter!
• dealtagger - Let all your friends know what your shopping for with the dealtagger > twitter update thingy!
• MyChores - Keep track of your household chores and send automatic Twitter posts whenever you complete a task!
• Manchester United News - Get Manchester United news straight to your mobile phone for free.
• GeoTwitter - This mashup uses Google Maps API and Twitter API. The most recent updates are fetched from the public timeline and mapped once every minute.
• Twitter Tube Tracker - find out when your public transport route isn’t running (London Underground and SF BART)
• twitterami - Use Frappr to see Twitter friends on a map.
• twittervision - Real-time display of the public Twitter stream on a map. Warning: dangerously addictive.
• Planypus, the place where friends make plans, now has twitter support! From any plan, click Post to Twitter to twitterize your plans
• Twitterholic: Top 100 Twitterers leaderboard.
• Twitter in 3D
• Twitter updates from Pluggd - Pluggd’s podcast player can automatically post updates to your twitter account… Let your friends know what you’re listening to!
• mibazaar - Current Twitter Posts on Google Maps
• Twitter Gadget - A Windows Vista Desktop Sidebar Gadget that helps you keep track of all the sweet tweets! Fetches tweets from twitter.com and updates them every 10 seconds.
• Twitter SpellCheck Bot - Lily program that lets you check the spelling of a word via Twitter.
• Twitget - a Twitter Gadget - This is a Windows Live gadget that can be hosted on live.com or on Spaces. On Spaces it shows your last tweet and on live.com you can use it to track up to 5 tweets from your friends.
• Twitter Planet - This is a Windows Live gadget that shows the Twitter public timeline overlaid on a Virtual Earth map. Can be hosted on live.com or Spaces.
• Viddler has some sweet Twitter integration allowing you to both syndicate your tweets to your account as well as post site updates to your Twitter account.
• Flitter: Flickr stream generated by the Twitter public timeline using this yahoo!pipe and rendered in vvvv.