There have been some really interesting battles going on in the URL-Shortener space since I've started compiling data on all the competitors.
The two giants are TinyURL.com and Bit.ly. Interestingly, Twitter changed their default shortener from the classic tinyurl, to the up-and-coming bit.ly (following their announcement of venture-back financing). As a result, bit.ly has surpassed tinyurl in daily usage for June.
The rest of the pack is orders of magnitude behind these two leaders in usage. Still, there are some interesting battles in the back of the field. Digg.com is ramping up following their innovative (but much maligned) toolbar. Ow.ly also seems to be getting some good traction on the strength of their Twitter application suite, HootSuite.