Basically, start at the top and go down: http://www.boardgamegeek.com/browse/boardgame
Settlers, Bohnanza and Carcassonne are excellent starters into the world of boardgames. Geeks will want to graduate to Caylus, Puerto Rico and the like later on.
I think they redesigned the game recently, so it's possible the new version of the expansions won't work with our original edition anyway.
These days, we're mostly into Puerto Rico, Ticket to Ride (various editions), Carcassonne (also somewhat luck-based), Power Grid/Funkenschlag and Agricola.
You should buy such extensions if you have played the basic game a lot.
Games also last longer with this extension, count on 3 to 4 exciting hours.
Since I'm on hackernews, I've always wondered when this game would pop up and what other board games you would advise. I'll have a look at Puerto Rico asap.
If you're just looking for a list of games to try, see http://www.boardgamegeek.com/browse/boardgame and start from the top.
Also, most (good) board game shops have an open play night where you can go in and check out whatever you want. This makes putting $80 down for that copy of Agricola much easier.
If you're in the greater Seattle area, Uncle's Games at Redmond Town Center has a game night on Fridays. They're also the best game shop around, imho (although I might be biased, they know me by name).
I'm pretty open and I guess I can't be disappointed by the top picks.
Yeah, I was lurking at Agricola and Puerto Rico but they seem similar to the Settlers of Catan (I may be mistaken).
If people like card games, I can also recommend the original Canasta. http://en.wikipedia.org/wiki/Canasta
PS. Hi from Netherlands ;)