WordPress has many plugins to shorten URLs but I am only going to mention few but the best wordpress plugins that chop URLs and make them short. Short URLs can be helpful in many ways, it allows you to share the content easily with friends also you can track how many times that URL has been clicked.

WordPress URL Shortening Plugins

Short URL Plug-in

This plugin not only allows you to create shorter URLs, it even allows you to track the number of clicks on short URLs.  This is even more useful when you give your users something to download, you can easily track the number of downloads and other link on your blog. This plugin also allows you to reset the counter and has lots of other features.

YOURLS: Your Own URL Shortener

I personally like this plugin. This plugin allows you to have your own URL shortening service. It creates a shorter URLs of your posts and tweet that on twitter as you publish the post. This plugin is easy to configure and it is also compatible with tr.im, is.gd, tinyurl.com and bit.ly for maximum fun.

WP-Chunk

This is a very useful plugin. Sometimes commenters share  URLs in comments in reference of their comment and this wordpress plugin will shorten that URLs so that it wont look ugly and when some user click on that URL it will redirect the user to original URL.

Pretty Link

This plugin is the most flexible plugin since it allows you to chop the URL of any web page and gives you the option to track the number of the clicks that has been made on that link. The cool part about this plugin is that you can use your own domain name to chop the URLs.

Short URL Generator

This plugin will automatically chop the URL of your posts so that you and your users can easily share the content on social media sites like twitter, friend feed etc.You can place the short URL in your post by placing this short code [shorturl] where you want the short URL to appear.

There are many other wordpress plugins available that does this work but I found them best and easy to use but if you know any another plugin that might offer some more functionality then do let me know by posting a comment.