Shorten Your URL with Forwarding

Webmaster Note: Personally I'd strongly suggest avoiding these to redirect to your website unless it's really needed (ie. a tweet with a long address) because not only will those hard earned links become worthless if the short URL service stops its service, the loss of branding is something very important to consider.

Also note that if the URL redirection service you choose is with cloaking (it covers your real URL), when you link out of your site, type target="_top" inside your links or your address will remain in the location box of your visitors browser the rest of the time they are on the web. Also some free web space providers have added a script that prevents hiding your real URL and will either redirect to the wrong page or show an alert box.

Tiny URL
This is one of the more popular redirect services since they offer handy stuff like a browser extension for Firefox that lets you quickly and easily add a TinyURL for any page you visit, and for Internet Explorer users there is also a convenient way to do this right from your browser.

EU.org
This free service is different than any of the others on this page. They offer a free subdomain urls, http://example.eu.org, but they do not provide hosting. It looks a lot more complex but may be a better option for some web sites. No advertising is added from what I saw, a link back is requested.

shim.net
Shim's free URL redirection service offers the ability to forward to dynamic IPs as well as other features and currently shows no ads.
Domains currently available:
yourname.shim.net
yourname.freegaming.org
yournames.freebiefinders.net and a few others. Caution: this one uses a 302 redirect (302 means temporary redirect and will cause headaches for you in the search engines.)

Bravenet
Bravenet offers a fast redirect, addresses are:
http://clix.to/yourname/
http://trax.to/yourname/
http://clik.to/yourname/
http://trak.to/yourname/
http://embark.to/yourname/ and many others.