Phillips screwdrivers are probably the most common, and look like an "X" at the tip. Phillips screw heads are used for machine screws, drywall screws, deck screws and more. Common sizes for woodworking are #1, #2 and #3, with #2 being the most common.
Flathead screwdrivers are also quite common, with a flat, spade-like tip. Flathead screws also come in #1, #2 and #3 sizes. Wood screws are often flatheads.
Other useful types of screwdrivers will drive square head screws (some deck screws use square head, as they're less likely to strip than Phillips), or six-pointed star shaped Torx headed screws. A few varying sizes of these will be useful, but not needed often.