This is a huge topic. You can find some great discussions about it at places like AWN.com, but the discussions are usually about landing freelance work. It is possible to sell already completed animations outright but I don’t hear about that happening very often.
Some folks use their animations for marketing their own DVD’s, teeshirts, etc., and/or generating ad revenue, but the main goal is usually getting it seen anyway you can for free in order to generate clients for freelance work and/or land a licensing deal (the ultimate). Viral marketing. If you create an animation that gets seen and shared by millions and people on TV are talking about it, you are definitely going to get some business offers.
It can happen -take for example the lady who started a simple website with 30 second movie spoofs with bunnies. She was approached by a studio and now her series is on television, and I’ve seen her interviewed on cable news.
There are some other avenues opening up online. Atomfilms.com pays royalties from ad revenue and distibution deals, and has invested in some works before they were begun. Most make petty cash, some make thousands, and a few have made $100,000.00 (so they say).
Everything mzungu and julesd-g6 said applies no doubt. It’s gotta be good (a subjective term -there’s alot of crap making it big simply cos it’s gross or offensive) and a bit of luck doesn’t hurt.
Edit: Here’s an interview of that bunny woman at Cold Hard Flash