The three most common measures of influence on Twitter are:
(1) How many followers you have
(2) How often someone re-tweets or mentions you in their own Tweets
(3) How many times people click on your shortened URLs, which contain useful analytic data (this is my favorite measure).
But here is a cool Twitter application that will let you know if people have added your Tweets to their own list of "Favorites" on Twitter. This is interesting data both in specific and in aggregate, usually it goes unnoticed because there is no built-in counter that broadcasts this information on Twitter (like Follower count, for example).
Just visit this URL: http://favstar.fm/. Then use the instructions on the interface to reveal your most popular Tweets and your most recently favorited Tweets.
What others ways do people like to measure influence on Twitter? Are there offline ways that any of you like to measure Twitter? Let me know in comments, or on Twitter itself, or by emailing me at firstname.lastname@example.org (make the subject: "Twitter Influence Blog" to help me see and respond quickly).