I purposefully left off any titles that are strictly wargames, although almost all of those are specifically for 2 players. Here is the list - in no particular order. I would have listed Ticket to Ride or Lost Cities first, if I was doing them in order that I would recommend.
Agricola - yes, latin for Farmer. Great game.
Carcassonne - tons of add-ons and variants, the basic game is great
Settlers of Catan - very good. The regular version is only okay for two (I think it is 3 or 4 players, normally) - but there are two versions of card games that are good. The dice game is also awesome, and travels well.
The Rivals for Catan (2 player card game - good)
Catan dice game - huge fun, easy to play, and who doesn't like weird score sheets, and dice with sheep on them?
Tikal - cool exploration game, there is a new version (Tikal II) that supposedly plays faster.
TransAmerica - fun, fast. Play several times in an evening. There is also a Europe (TransEuropa) version.
Lost Cities - best game for couples, ever.
Saint Petersburg - Good. Not as much as some others, but some interesting strategies.
Hansa - great game, and fun. The Author (Michael Schacht) has a great website, with some variants (free to print) available.
Web of Power- from same author as Hansa - I like the medieval version, it is out of print (but free on his website) - but available as "China" - different theme, different board.
Attika - excellent game. Can be a little competitive, but still fun.
Caylus - interesting medieval theme. Collect resources, and place workers, to builds a village around a castle.
Pillars of the Earth - worker placement game (similar to Caylus, above, and Stone Age, below). Lots of references to the Ken Follett novel.
Stone Age - fun worker placement game. All three of these (Caylus, Pillars, and Stone Age) play different enough to each be fun.
El Grande - very strategic. Gives some people a headache to play, but I like it. Not bad with 2 (rules variation) best with 4 or 5.
Terra Nova - fun. Also fun with three players. A little more strategic than some others.
Pandemic - cooperative game. Hard to win. I love it. Anita hates it. Enough said.
Through the Desert - build networks of plastic colored camels. Much more fun than it sounds, and the camels look like pastel candies. Good for 2,3,4 or 5 players.
Ticket to Ride - best intro game to Euro strategy games (all of those listed here). Lots of variants. Either USA or Europe are the best place to start. Nordic Countries is good for 2 players, but so are the others, and Nordic Countries has some weird strategies.
Small World - fun fantasy "wargame" - super light weight, but lots of interesting combinations.
There are others. For instance, I really LOVE Power Grid - but it is a super analytical game (then again, so is El Grande). But I didn't include it because it can be a bit unforgiving. That isn't so much fun in a couples game.
