There are many forms of online RPGs, from the interactive community centered around a java applet game that is Dragon Court to the more traditional RPG played through email and such forums as Macrays Keep. And then of course there's the old school answer to online RP, multi user domains, or MUDs.
Let's face it, from the moment the internet became available to civilians (it was originally a military project), gamers have been using it to connect to other gamers hundreds, or even thousands of miles away. It's the nature of the hobby I suppose. The internet has made it possible for us to have something akin to GenCon, were we meet and play RPGs with people we wouldn't ever see otherwise, every day. Granted, GenCon's still better, but it's nice to just connect to people.
Dragon Court, partially because of the extreme involvement I had in it at one point, as a whole page on my site dedcated to it's description.
Macray's Keep is a place where you can go to play RPGs the old fashion way. You say what you're doing, use the online dice program, and the game master at the other end of the internet connection tells you what happens. Sometimes it works through chat rooms and sometimes through forums, but it just works. Practically any PnP RPG ever made can be played there.
The Mud Connector is the place to go if you're interested in MUDs. These nifty little telnet accessible programs allow you to tell the computer what you're doing and automaticlly output the results. If you walk around, you end up in other rooms. If you attack somethign, it fights back. These range from fantasy settings, to rifts muds, to pure player vs player action like GodWars MUDs (my personal favorite). Oh, and if you're going to get into muds, stop by Zugg Software and pick up Zmud. No mudder should be with it or a similar program.
Dragon Court