That seems to be the question these days in the age of Twitter. Because Twitter only allows 140 characters per tweet, it is a good idea to use an URL shortener to save as much space as possible.
And there are a lot of good services out there that will not only allow you to shorten your URL, but even track how many clicks came through the shortened web address. TinyURL and bit.ly are among the best URL shorteners. And if you really want to get fancy, you can use awe.sm to customize your shortened URL, though it will set you back $99 a year.
One important but often overlooked feature of these services is the type of redirect. The 301 redirect tells Google the page has moved permanently, which means Google will count the link as pointing to the actual destination. This is important if you are posting a link to an article as it effects search engine optimization (SEO).
Perhaps the best question is whether or not you should be shortening the URL in the first place. Using one of these services is great for posting links on Twitter. After all, the standard URL will take up most of your message if not shortened. And they can be great for sending a link through email when the full URL might get cut off. They are perfect for Facebook updates and instant messages.
But that's about where they should stop. Occassionally, I'll see a blog or an article use a shortened URL as a link rather than the full web address. Heck, I've even seen this done on the New York Times website.
Here's the problem: there is no guarantee that a year from now that URL shortener is going to be around. Right now, they are all the rage with Twitter's popularity going through the roof, but don't expect all of them to be around for years and years. And what's going to happen to all of those links when the company is no longer around? Those 301 redirects turn into 404 page not founds.
So if you are writing a tweet, go for it. But for blog posts, articles and basic web content, stick with the full web address.