According to Marshall Kirkpatrick of ReadWriteWeb Twitter has "crowned Bit.ly the King of all Short Links" and replaced TinyURL as the default URL shortening service that Twitter uses. (I’m cdevroe, btw)
Scaling Bit.ly to keep up with the demands of Twitter, since Twitter is growing at a remarkable rate, is an obvious concern. Will Twitter buy Bit.ly to help scale/fund it? I hope they do. Not only because I like Bit.ly – but because then I could say I told you so.