Nagas are also frequently depicted as being capable of transformation, from one extreme of being entirely snake to the other of entirely human. The legs would obviously have to turn into snake all at once, but any amount of the torso could be snake; also, the naga could have arms or not. In fact, depictions of non-transforming nagas vary as to whether they have arms.
When nagas do transform, it is quite different than the transformation one usually expects out of werecreatures. If a were has a partial transformation, it is usually not spatially dependent. According to AD&D, the naga transformation is completely different, being a dimensional process rather than a polymorphic one. Thus, it is unhealthy for a naga to jump into a bag of holding or portable hole, while a werewolf would have no trouble. This is one of the few contingencies not programmed into Nethack (at least, not as of version 3).
Since nagas were ripped out of their original mythos, they have been placed into a wide variety of settings far removed from rivers, including the deserts (one AD&D species overview), in elaborate tunnels under mountains (in Xanth), etc.. Nagas have also typically undergone an unfortunate personality shift from wise to borderline sentient and bloodthirsty - typical RPG monsters. As a friend of mine said, "What else do you expect a young naga cleric set loose on the world to do, besides FSU?"
Things that are much like nagas are depicted (in the west, at least) more often than outright nagas. For example, Medusa in Clash of the Titans. While the general form of having a snake tail fits uniquely enough to throw her in the naga-like bin, she has snakes for hair (actually, for Medusa, snakes-for-hair is common, while having snake-for-legs is unusual).