A bunch of new Twitter accounts popped up in our newsroom recently so I put together a quick list of resources for people just starting out.  I use all or most of these services:

Track your growth
http://twittercounter.com

Get your stats
http://tweetstats.com

Get recommendations for who you should be following
http://www.mrtweet.net

Get notified when people stop following
http://twitterless.com

Find out how influential you are
http://twitter.grader.com

Look for connections among your followers
http://www.tweetwheel.com

A live map based display of everyone
http://twittervision.com

Find more friends
http://whoshouldifollow.com

Search Twitter
http://search.twitter.com

Make shortcuts for URLS (and track the clicks)
http://bit.ly