Board Game Arena is best arena
Board Game Arena is the best website for boardgames I've found. They don't have everything (In fact, they have nothing that has its own version online already, so no Catan or Dominion or Carcassonne etc.) but they have a lot of games, and they are mostly very well implemented.
Lately I've been playing Race for the Galaxy, Puerto Rico, Caylus, In the Year of the Dragon, Seasons, Tokaido, Stone Age, and Sobek, and there are dozens of others I've yet to get into.
It's great for when I have a half-hour between classes or something, or when my students are taking a test, I can pull it up and play a quick game of something (usually Tokaido when I want something fast) against some strangers. I'll also play in the evenings sometimes when I see buddies online.
The best feature, imo, is the turn-a-day gaming mode, (though they call it 'turn-based' on the site (versus 'real-time') though it's a misuse of the term). In this mode, you can play any of their boardgames asynchronously with your friends, just logging in once/day to play your turns in whatever games you have going. It's like GMR for boardgames. I'm usually in about 12 games at any given time.
You can 'friend' people on the site, and form groups to facilitate invitations and to create join restrictions. I've started a group for my boardgaming friends on there already (The Mitey Worriers group). It currently contains @Zanthian, @CrazyJoe, @GHoosdum, @Adrestia, @Colgere, and myself. We mostly have the same usernames there as here (I'm 'CB Droege', since 'CB' is too short for them, and I think Joe has numbers on his name).
Go take a look.
If you join up, or are already a member, post your username here, so we can be friends, and I can invite you to the group. If you invite me to a turn-a-day game. I will likely accept.