A Virtual Tabletop (VTT) is an application suited for playing pen-and-paper RPGs online. Unlike simple chat programs with dice rolling features (like IRC), VTTs usually include mapping tools for placement of tokens, automated character sheets, 3d dice, and other functions.
VTTs vary in scope, utility, and popularity. Currently, the most-used VTT by /tg/ is Fantasy Grounds, followed by OpenRPG.
Note: Please be certain to pick up the Development version, as it contains far more features and is actually updated more often than the 'stable' or 'release' versions.
Note 2: Do not add your personal image folder (e.g. your 4chan pictures) as a resource library or you're going to lag into oblivion. Make a separate folder and drop images you wish to use into that single folder instead.
MapTool is the second-most commonly used VTT on /tg/. It's a clean application that takes little time to learn and allows for easy modification (without even a smidgen of programming knowledge) to modify to fit any system. Its token-based approach to information tracking means having easy-to-recognize symbols sitting on a physical map that hold all the information you need, so you don't need to sift through sheets of crap to find the right info. Players have a lot of control over their own tokens and as much control over the world as the DMs allow. I simply like it more than the alternatives.
The RPTools suite consists of four programs: MapTool, the client/server application; DiceTool, a complex dice rolling utility; InitTool, for streamlining battles for DMs; and TokenTool, for easily making tokens of varying sizes. DMs will want to grab all four of these items, whereas players only need MapTool (and are recommended to get TokenTool).
Find it here: Vassal Engine
A boardgame and card game simulation, used for anything from 40k to Candyland.
(Info removed for being massively outdated)
Find it here: OpenRPG.com
OpenRPG is a free VTT written in Python. It is the third-most used application on /tg/. Unfortunately, I haven't used it much so I can't say much about it.
Find it here: Gametable
Deltoid Maximus helpfully provides the following synopsis for Gametable:
Gametable is a beginners VTT. It's slightly easier to use than MapTool, but not nearly as in-depth. The Interface is kind of murky, but easy once you know what's what.
With the right resources, you could make complex maps, but it lacks neato things like fog of war or built in characters. All it has is a chat window and a game window.
Gametable is good if you're going for a quick use, but if you're going for looks in your game, use something else.
Find it here: Paranoia-Live.net
JParanoia is a free VTT for the Paranoia RPG. I haven't used it, but if you're looking for some Paranoia, go nuts.