You'll get almost no argument anywhere if you say that bouillabaisse is the most typical food of Marseilles—and you'll get nothing but argument if you try to discuss its origin and "the" recipe. As with most foods that originated among poor people, and of necessity, this fish stew has no single chef who invented it.
It had its origin among Marseillaise fishermen; it starts with the bony rockfishes of the Mediterranean that came up in the nets but had no market among those who could afford to buy others. It's almost always made with several kinds of fish—Julia Child believed that its success was based in part on the Provencal spices and olive oil and a mixture of fish: "lean (non-oily), firm-fleshed, soft-fleshed, gelatinous, and shellfish"
The one fish no one disagrees on is rascasse, a bony rockfish common in the nearby calanques. Next in line, sea robin (grondin) and conger. After that, what you will. In Marseille tradition, the broth is served with slices of bread with rouille, a spicy mayonnaise, and the fish comes separately to be added in or eaten separately. The name has nothing to do with the ingredients, by the way: it's a corruption of words from the Occitan language meaning "boil, then simmer." MORE on this history.
We had ours at Rhul, a rather pricy but well-recommended place along the Corniche at the eastern end of Marseilles that has specialized in bouillabaisse for three generations.
I, only recently a fish-eater at all, went with considerable trepidation; my wife, an experience fish-eater was also unsure how she'd feel about the fish involved. We were both pleased that our fears were unfounded: a delicious and filling meal, served with ritual by a staff that seemed pleased we were happy (although conger turned out to be our least favorite).