Settlers of Catan is a really awesome board game created by germans. They make some neat games. If you don't know what it is, I think you'll like it so you should check it out. I heard there is an online version but I don't know much about that. I think the game is similar to risk but more easy going and doesn't take as long to play.
and as a bonus...the board changes each time you set it up!

Geister Treppe or Spooky Stairs is also a good game. It is a childs game...it won the childrens game of the year in 2004 or something like that...but it is equally good for adults! it is a simple but fun game.
settlers is a good game, its not like risk though.
Its 2-4 people and you are able to buy extra for 5-6 players.
The game doesnt have any battles like risk does, its a building/trading/tricking people to do things that you want them to do kind of game.
there are other boards that you can buy that expand the game and how its played, but its still fun none the less.
While I am a huge fan of settlers, I have been more consistently impressed by the games imported by Rio Grande Games.
Web of power is an excellent beginners game, While "Princes of Florence" and "Traders of Genoa" are excellent for experienced gamers and casual gamers alike.
My favorite of their games was unfortunately purchased by Hasbro, who refuses to release it. "Traumfabrik" aka "Dream Factory" is a game about old school Hollywood, and is amazing. If anyone can manage to get their hands on an imported copy, I highly reccommend it.
trikstott, those sound like neat games too. i hope i can check them out sometime.
i also like medici (sp?) have you ever played that?