So cooperative or semi-solitaire where you try to reach a high score are preferable to games where you actively have to kill each others mens? And not too complex?
Off the top of my head:
Lost cities is a 2-player card game. The mechanic is draw a card->place a card and you compete to collect as complete sets as possible in 5 colours to score points from an expedition. It's cheap and we often play it inthe boardgame club I frequent when 2 of us are waiting for another game to finish so we can start something new. There's equal parts gambling, paying attention to what your opponent is doing, counting cards and luck of the draw involved:
http://boardgamegeek.com/boardgame/50/lost-cities
Starship catan is another 2-player card/boardgame. You compete to upgrade your ship and gather victory points. There's about equal parts luck and skill involved as you have to remember which cards are in what pile. Player interaction is lowish as you're mostly racing to see who can build up VP fastest. But there are a few oppertunities to steal the other persons resources and trying to get the good cards first.
http://boardgamegeek.com/boardgame/2338/starship-catan
Carcassonne plays best with 3-4 people, but is decent with 2 or 5 as well. It's a tile-laying game where you try to build the most profitable areas to occupy with your little dudes. There's a ton of expansions for it, but I feel most of them detract more than they add.
http://boardgamegeek.com/boardgame/822/carcassonne
Small World is another game that really works better with 3-5 people, but it does have a 2-player board as well. It's a nicer-looking and slightly better balanced version of the old classic Vinci. Smallworld Underground is (in my opinion) slightly better than vanilla, since it introduces objectives to capture that grant additional abilities. The rules may seem daunting, but I managed to explain this stuff to my grandparents a while back and they really took a liking to it. It's territory control and you kill each others little dudes off. It may or may not be a turn-off for the missus. But again, I've introduced this at family gettogethers and even my grandparents don't mind killing off my nieces berserker hobbits.
http://boardgamegeek.com/boardgame/97786/small-world-underground
Pandemic is a strictly co-op game, which you mentioned you were after. I'm not a big fan of it myself, but a lot of people sing its praises. The players work together to contain and eliminate virus outbreaks. I once saw a 40K fan remake of it called "CLEANSE THE GALAXY!" which was pretty awesome, but GW shut it down.
http://boardgamegeek.com/boardgame/30549/pandemic
Elder sign is a quickie version of Arkham Horror where players team up to defeat a lovecraftian old one. The setting may be a turn-off. I only played this once, but it was pretty fun. We were 4 players for it, not sure how well it'd work with 2.
http://boardgamegeek.com/boardgame/100423/elder-sign