Their introduction of the service here mentions some of the points: remember the last 15 short URLs you created, click/referrer tracking of the bit.ly short URL, an API for creating short URLs from your web page,  thumbnail images, automatic free mirroring of each of your web pages if they're visited via bit.ly (saved on Amazon's S3 storage, apparently, which should make this a reliable offering).

Promisingly, they seem to have plans to actively keep beefing up the bit.ly features. A really nice feature, introduced only a week ago (late August 2008), is the bit.ly bookmarklet for Firefox.

You open the bit.ly page inside a Firefox window, and locate the bookmarklet as shown by the red arrow below:

Simply drag the link to your Firefox bookmarklet bar (the wording "to you browser toolbar" is s little ambiguous), then open a web page in the Firefox tab, and click on the bit.ly bookmarklet (circled in green below), like this:

Then, a moment later, the shortened URL appears in the very same Firefox tab:

Easy, eh? There's no similar add-on for Internet Explorer yet (and maybe, ever) -- Nor the new Google Chrome, naturally enough... That's another pat on the back for Firefox's extensibility!

I haven't been using TinyURL so far, and in light of bit.ly turning up on the scene reckon that I'd rather use it. Take a look, perhaps you will too.