Everyone's stressing the chef's knife, but I'd be even more generic; when starting out, you can do almost every task with:
- A large knife (8" Chef, 7" SantokoJapanese Santoku, or a Chinese Cleaver)
- A small knife (Paring or similar)
- A bread knife (serrated, 10" or longer)
As you add to your collection:
- A boning / filet knife
- Kitchen sheersshears (for snipping herbs without a cutting board or cutting the back out of a chicken)
- A carving knife (for slicing meats and large melons or splitting a cake into layers)
- A heavy cleaver (so you don't mess up your main-line knives when hacking up bones; heavy enough to use the back of the knife for cracking a coconut)
- A utility / tomato knife (mid-sized, serrated)
A few people have mentioned a larger chef's knife, but it's going to be harder to control. Develop good knife skills first, then move to something larger.
I know a few people who do everything but bread with a paring knife (and no cutting board, in their hand, cutting against their thumb), and I'd consider them "serious chefs" (southern, over 60 for the most part, but also a few apartment living europeans-living Europeans).