Third party candidates do run, but they rarely get a signifigant percentage of the vote, and even more rarely win, at least in the national elections. Third party winners are more common in state and local elections. There are two third-party US senators right now, but the last third party president that I can recall was Theodore Roosevelt, about a century ago.
The ballot requirement vary from state to state, I believe, but they generally require a certain number of signatures from registered voters to get a candidate on the ballot. Generally here in Oregon I've seen candidates from the Constitution, Green, and Libertarian parties on the presidential ballot.
I have to say that the more I find out about Obama, the better I like him. I'm actually having second thoughts about Edwards now. Edwards is a fighter, and I am spoiling for a fight myself, but Obama may be more appealing to voters with his message of hope and an end to partisan infighting.