There's an on-line multiplayer wargame on the web called Warlight. The client software is implemented in Flash and runs in your browser.
http://www.warlight.net/
It reminds me quite a lot of Risk. It's different, though, in that you can control the amount of randomness involved in the battles, there are a few more features like extra types of cards, and the mechanism of giving orders and then having them executed in a separate phase is reminiscent of the game Diplomacy (not exactly the same, though). There's also an optional fog of war feature, where you don't see the parts of the map you have no troops in or adjacent to.
You can play it for free both against AIs in tutorial and practice scenarios, and against other humans in fast or slow games. Slow games can, for example, require you to move once per day or whatever schedule you get the other players to agree to.
There are small and big maps, so you have your choice of how long a game you are going to expect. It's possible to buy a subscription which gives you some extra options in how to set up new games and such, but it's quite all right to just try the game out without spending anything. (I'm at just trying out phase myself.)
The mechanics are pretty simple and quickly learned. You should pay attention to some details to find the best strategies, though, as always. The tutorial level you find in the single player mode is quite a good way to learn the game. It's also pretty quick to play.
For those interested in details of development, here is why the author switched over from Silverlight to Flash. This background detail also explains the name
http://blog.warlight.net/index.php/2011/01/why-warlight-switched-from-silverlight-to-flash/
I tried searching the forums both with Google and the internal search mechanism, and no results came up. So, I guess this hasn't been talked about.
[Last edited by Pekka at 11-12-2011 06:35 PM : corrected typo]