There is a way to actually play pen and paper RPGs online. The best website (as far as I feel) is Roll20.net. This website acts as a virtual tabletop, where you can play a number of pen and paper RPGs, with all of the dice already on the website. Plus, you can play with people from all over the world, with voice chat and many other fun gizmos built into the system. When you’re signed in there is a link, up near the top, where you can find campaigns you may be able to join. Here is a link to the looking for group forum. This forum shows starting and current sessions that are looking for extra players. You can select time and days you are open for play, and look for numerous games, or just a one shot adventure. If you are new to a game, you can even narrow the results to sessions designed to be friendly to first time players.
With this website, I would also suggest you try using Myth-Weavers to create your character sheets, since most Online Game Masters like to have all of the player information available to them. This website makes it easy to share your current character-sheet for a large number of games online. Most of the math is also automatically done, to make character generation faster, and since it is a free online software, you save a lot of money on paper and ink.
However, back to the topic at hand, if you really want this personal connection that you make when playing in person, I would suggest that you look up your local hobby and comic book shops(online locator linked), as they tend to host one or two RPG games every week, and even if they don’t, it is likely you will find someone who knows where to find such games. If you don’t know where the hobby shops are, or the players there are simply too advanced for you to keep up (happened to me the first time I went to one), NearbyGamers is a very good place to start. It has a large selection, and it makes it easier for you to set up in person meetings.