Roleplaying games are very hard to describe concisely, mainly because of the incredible variation you can achieve within a given set of rules. If you want to learn about these, please let me refer you to a rather nice document that I managed to discover while flitting. The Art Of Adventure. As I feel that I can't really mention any specific brand names, you may wish to know exactly what system I use. Here is one that I found quite refreshing during my off hours. It is on several of the lists of resources which appear below, but does not really (in my mind) have as much fame as is due to it.
Good sources that I have found are:
Of all of the above, Coron's Sources was my overall favorite. Even though Coron has left the picture, his list has the most and the best of everything that I have seen around. Although more then the average number of links are bad, the remaining ones are of much higher quality then the norm. With something for everyone, I would prefer it greatly to my minimally readable site.
More Specific Topics:
Online means you are tying up valuable communications lines the WHOLE time you are playing. These are usually at least partially real-time, with 15 minutes perhaps mapping into a game day for some. There are many different kinds of these, but the only ones that I am describing are free, or were as of the creation of this page.
Computer (-Based). You download these and then play them on your computer. They are usually not as violent as some (a.k.a. d 00m), and are also comparetively cheap (free, usually). Some of these take years to complete, as they are very difficult. However, many of these are not true roleplaying, as you can not really do truely arbitrary things. But, for computer-based game intellegence, they are reasonable. A few of the newer versions of some of these games have stopped being backwards-compatible with old systems- THEREFORE, Don't download Nethack321, or NetHack310 if you want to run it on your old clunker. Try using something that takes up less space then its documentation, if you can find it. I have found that the most enjoyable games are usually less than 1.44 MB, and ones larger than that usually aren't as good (per pound).
Paper and Pencil. These are the traditional games of yesteryear, where a player sets off on a quest (with the assistance of a gamesmaster) to (usually) commit senseless acts of violence against innocent denzins of a foreign terrain. These are really good if you can find a reasonable or experienced gamesmaster. If you do not have any friends, you probably don't want to spend much time on these as you usually need a minimum of two people before you can do anything (and at least four before it gets really interesting). However, this type of game usually requires much more of the players (and gamesmasters!) than the others.