There’s an enlightening conversation taking place on Hacker News about just that subject. The short is, they don’t make any money.
They don’t. To be honest the majority of url shorteners don’t make any money at all. I know because I run one.
It costs me nothing to run because it uses next to no resources on a server that I already pay for and I got the domain for free.
The long answer is that they don’t, but that they don’t cost much to run and hopefully, someone, someday will think of a way to make money with them. The HN discussion seems to be centered on one unproven method of profiting: market research.
# Think: pulling that data into a techmeme.com style aggregator/ranking site for the most popular urls people are linking to. Imagine how dynamic it would be – things that got linked to the most would percolate up to the top. you could watch in near real time as news breaks and gains traction.