It made sense back before Twitter had one of their own. And I know that some people use it to get link analytics. I've also occasionally seen it used for printed materials, to get pretty URLs that are easy to hand-type.
People also use it for malicious purposes, such as hiding malware, or disguising referral links, or otherwise trying to obfuscate where a link is going. (Note: I'm not calling referral links malicious, I'm calling disguised referral links malicious.)
Other than printed materials (which need pretty URLs and thus often need a dedicated first-party URL shortener) and analytics, what are people using third-party URL shorteners for today?