TweetBurner and Bit.ly, among others, allow you track clicks on your shortened links.
Yes, you can track how many times people click on your shortened link.
From the different choices out there I’ve only tried TweetBurner (www.twurl.com), the one I use, and www.bit.ly, another popular choice.
Here’s how to set it up so you can track your shortened clicks usign twurl.com, regardless whether you shorten them at the site or through an application like TweetDeck or Twirl:

Create an account.

Link your accounts

For TweetBurner, select "twurl" in your desktop application.

Check the number of clicks.
While writing this post I’ve noticed that TweetBurner seems to count “robots’” clicks while bit.ly doesn’t. In other words, bit.ly seems more accurate. I will be using it from now on.
If you use any other service or have more to add, please feel free…
Tags: strategies, tweetdeck, twirl
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UPDATE
After using bit.ly links for a while, I have to say, they’re way better than twurl. I’m sure twurl is going working to catchup but, for now, bit.ly is the way to go.