Good gateway board games
Carcassonne (FTW Eric) is a good one. Very simple and easy on the eyes. As Enron suggested, Settlers of Catan is also really great. When choosing, basically ask yourself "Do I need to roll dice?" If you do, go with Settlers. Otherwise go with Cacassonne. Better, pick them both up, yay!
If you're playing with the wifey, there's probably not much chance you can get her into a game involving combat at all, but if she's flexible, or if there is someone who might be into the theme, Memoir '44 is GREAT. It's a simple, very fun boardgame with a WWII theme. It is literally impossible not to like. It plays quickly, has neat little plastic soldiers, and it's fun to play the abstracted versions of various battles.
Acquire is also fun. That game is somewhat mainstream so you might have seen it; it's also easy to find since Hasbro/Avalon Hill currently publishes it. A game about building hotels where there is a stock buying/selling mechanism.
Two fun ones for lots of people (four or more) are Bang! and Saboteur. These are both conceptually similar games in that each player is either a good guy, or a bad guy. In Bang two-three players are outlaws and the other players are the Deputies and Sheriff. In Saboteur everybody is a miner trying to dig tunnels to some gold. Two-three players are secretly saboteurs, trying to keep everybody from getting there. In both games, the roles are dealt out in secret at the start of the game, people try to keep their roles secret (usually badly), and hijinx ensue.
Update: And lest I forget one of the best of them all, Ticket to Ride is a super-fun game about building train lines across the U.S. of A. It along with Memoir '44 is one of the few games that I would call impossible to not like. This game, along with Carcassonne, is the one that I play most often with my girlfriend.
While we're on BGG, I might as well pimp out my board game list one more time.
OK and Eric. Carcassonne? After YEARS of hate? Carcassonne? Wow. Go ahead and deny Puerto Rico all you want. You'll come around, sooner or later. It's gonna be the biggest gaming upset since the Great Ragnar Miniatures Addiction of 2005.