Here is a list of some of the more popular smoking woods people use.  There are plenty others out there, but not all wood is good or safe to use for smoking, so do your research before using anything that is a bit exotic or you are unsure about.

Type Characteristics
Alder Very delicate with a hint of sweetness Good with fish, pork, poultry,and light-meat game birds.
Apple Slightly sweet but denser, fruity smoke, excellent with pork.
Apricot The flavor is milder and sweeter than Hickory. Good with most meats.
Cherry Slightly sweet, fruity smoke flavor.  Good with most meats.
Grape Aromatic, similar to fruit woods, good with most meats.
Hickory Pungent, smoky, bacon-like flavor and most common.  Good for all smoking, especially pork and ribs.
Maple Mildly smoky with a little bit of a sweet flavor.  Good with pork, poultry, cheese and vegetables
Mesquite Very strong flavor, best with beef.
Mulberry Sweet and very similar to apple, good with pork.
Oak Very popular, heavy smoke flavor.  Good with red meats, pork, fish, and heavy game.
Peach Slightly sweet, woodsy flavor, good with most meats
Pear Slightly sweet, woodsy flavor, good with game birds and pork
Pecan Similar to hickory, but not as strong, good for most meats.
Plum Mild and sweeter than hickory, good for most meats