According to the Larousse Gastronomique, the dish originated in the Provencal city of Marseille, and the classic variation has to swim with scorpion fish or rockfish to be authentic. Other shellfish, including small crabs and mussels, can be added, and If you're a high-rolling city-dweller, you can also toss in lobster and langoustines. Spices and herbs are added and then the whole thing is boiled together in a big pot.
The variations have increased over the years, and purists apparently dedicate a lot of energy debating what makes a true bouillabaisse. It'd be nice to jump into the debate...if there were any Denver restaurants where you could actually get a big bowl of the stuff.
If you know where to go, toss your thoughts into the comment section below.