A few I enjoy that haven't been mentioned:
Nexus Ops - this game plays pretty quick, and it has the unique quality of playing well with three players. I only have two regular gaming buddies and its a real pain finding games that play well with three players - either they play a lot like solitaire (Dominion) or they become a big exercise in clobber-the-leader (Shogun, etc). Nexus Ops has hidden missions that score your victory points, so attacking other players usually involves trying to satisfy a mission requirement and not so much beating the living crap out of them. The net effect is a lot of fun skirmishing, with frequent all-out battle royale's over the central tile. OTOH, the secret missions make the game a bit strategy-lite - since you don't know what motivates the other players, its a bit hard to counter them.
Race for the Galaxy - this plays very similar to Puerto Rico. We found the sci-fi theme a lot more engaging however. The biggest difference is that RftG uses a lot fewer game pieces, replacing nearly all pieces with cards, which makes it much easier to set-up and tear down. I haven't played enough of either to really comment on/compare how different/deep the strategy goes between the two though.
Carcasonne - this is a pretty simple game and not quite my usual taste (which runs a bit closer to Arkham Horror or Shogun/Samurai Swords), but it has several qualities that I enjoy - its very portable (I carry mine around when I travel in a big plastic bag), its easy to explain to and attract people that don't normally game, and it plays in a very reasonable amount of time. When you have mixed company looking for a simple game to play this one fits the bill. Typical play with newbies is to play without farmers in the 1st game, and explain farmers before you tear down the 1st game's pieces, then play the 2nd game with them.
Since I've mentioned it several times, Shogun, aka Samurai Swords, is a fantastic wargame that my friends and I often played instead of the original Axis and Allies. It has some ugly components to it however - as a free-for-all it involves a lot of diplomacy (and thus, various levels of backstabbing) and sadly there are incentives for outright eliminating players. I've seen plenty of feelings hurt, as well as people sidelined for hours by an early exit. When it goes well however we've had some really epic games. 4 players seems to be the correct amount - fewer, and you get clobber-the-leader; more, and you tend to have early exits from players with poor starting positions/grasp of the game.
Lastly if you are a Scrabble fan, try Bananagrams sometime. Its a lot more fun I think, and super portable for trips.