There are many ways to get around Thailand. Although most travelers choose to fly between the major tourist centers of Bangkok, the northern hills and the southern beaches, there's something to be said for the alternatives. There are still some special and out of the way places you can't get close to by plane, not to mention that most tourist cities have been turned into something which is not quite Thailand. To see the "real" Thailand you need to get outside the major tourist areas, which you can easily do by bus or train.
Here are links to the major transportation methods for inter-city travel. For information on getting around specific destinations, see city city guides.