Yesterday I pointed out how Wizards will be introducing an online tabletop experience to its 4e release of D&D. Wizard's idea is hardly the first in online "rules-free" tabletop gaming.
All of these systems allow one player to make a map and populate it with things. Players can make their own figures and place them on the map. Either the players or the hosting player can then move the figures around on the map.
All the systems have simulated dice-rolling. Often it's the best developed part of the engine, with fancy dice spinning around and them coming to a stop. Players seem to love rolling dice.
The most well-known is probably Vassal Engine. Vassal is used by hundreds (thousands?) of war gamers around the world to play games. War gamers in particular need the access to like-minded players ready to play very long games. I've heard nothing but good things about it, and I can't see why it couldn't be played for board games as well. It's Java technology, however, which might already be considered old-school.
Other systems, like Wizard's new system, are dedicated to RPG players. RPG players tend to lose interest in the game after moving away from their old group or getting married and having kids. They can no longer spend dozens of hours every night playing. Therefore, a tool that lets them cut out the travel time and saves the state between games contributes to solving the problem.
RPG systems generally include PC generation and customization and may also include pat animations or graphics for spells, events, or monsters.
Fantasy Grounds already looks pretty advanced and seems to do most of what Wizards' new tool will do.
ViewingDale - is fairly basic.
Tabletop Network (Gabob) by Tim Fowers is designed specifically for board gaming. It's being developed as I write, so send him your suggestions.