Does it matter which URL shortening web service you use when shortening URLs? Why will one choose, say TinyUrl over any other? And is their a lifespan for the shortened URL, will there be a guarantee that it will always be available after it is created?
Jeff Atwood wrote that URL shortening is destroying the web. His argument is that URL shortening distorts PageRank.
The internet is the house that PageRank built, and it's all predicated on hyperlinks. Once you start making every link your special flavor of "shortened" link, framing the target content -- heck, maybe wrapping it in a few ads for good measure -- you've completely turned that system on its head.
The short answer is, there isn't.
This has been recognized as a serious long term issue by many, and as such, an Internet Archive related project called 301 Works has sprung up to address this basically by providing redundancy to each providers records in case one disappears.
Personally, I'd stick with bit.ly or tinyurl.com as they are the best and oldest (respectively) out there. The fact that Twitter currently relies on bit.ly to shorten URLs through Twitter.com speaks volumes.
If you're creating the links and you want to be able to track activity through that link (maybe as part of a marketing campaign), then I'd recommend bit.ly. If you take any bit.ly link and add a + symbol to the end of it, you can get a bunch of stats about how that link has been shared on Twitter, how many people have clicked through etc
I agree with Kyle's point about picking a well known service for trust reasons, bit.ly is the default shortner on Twitter and very well known, so no problems there.
If you use Google Apps, you can set up your own Short Link service (available in Google Apps Marketplace, by Google Labs)... that way it's up to you which links keep working and for how long. You have to set up a new subdomain (something short like s.example.com) and then you can make short names for any page on the Internet. You also get to see a basic usage count.
I've set mine up so things like this work just fine: http://l.x3ja.com/diy-se.
A lot of apps have a url shortener built in, which explains why some people use some obscure ones.
For instance HootSuite (a Twitter 3rd party app) has a shortener for new posts, and the output is in http://ow.ly format. Many companies are getting into the game (ie NYTimes) -- perhaps for traffic analysis for their own purposes?
If you want statistics for your links... the StumbleUpon folks released a shortener and stats package at su.pr (all followed shortened links are placed in a StumbleUpon frame).