Rummikub is a good two-player game. I’ll second the motion for cribbage as well.
It’s not exactly Go, but I do have a Pente rug at my parents that I’ll bring back next time I’m visiting. I also have an According to Hoyle somewhere, so cribbage is definitely in.
Military history is a big common interest. Fantasy and science fiction to a lesser degree. Oh, I’ll also pick up a big box o’ classics.
Haven’t had a chance to play yet but the box for Munchkin Quest states a minimum of 2.
I strongly recommend O.G.R.E.
My friend, you have a world of games to choose from.
I would recommend every game I listed to you, then. Decide which era you’re interested in and go from there. The games I listed and their eras/subjects:
Twilight Struggle: Cold War
1989: fall of communism in Eastern Europe, 1989
C&C Ancients: base set is First Punic War, expansions later
C&C Napoleonics: base set is French, English, and Portuguese, expansions add other factions
Wilderness War: The French and Indian Wars/The Seven Years’ War
Hammer of the Scots: Edward I’s wars in Scotland
Unhappy King Charles: English Civil War
The Lock n’ Load titles should be self-explanatory
If you have other periods of interest, I promise that there are games out there for them.
Wargaming has picked up tremendously in the past decade (I suspect because baby boomers/Vietnam vets are retiring, but that’s a WAG). The last few years have brought a significant improvement in components and design. For instance, when looking at a game, you might see that new editions will have “mounted maps” where older editions didn’t. That means that the new edition has what you would think of as a “game board,” while older editions had maps not unlike you’d find as foldouts in National Geographic.
But it’s still a very niche market. Games come into/go out of print fairly regularly. One of the best and best known of these small game companies is GMT. GMT runs what it calls the “P500” system. They’ll license a game, wait until they have at least 500 orders, and then print the amount ordered. After the print run, they’ll wait until they have at least 500 more orders. Some games rarely go out of print. Some games stay out of print for years.
I will highly recommend GMT, by-the-way. Some games are better than others, but they don’t make bad games in my experience.
Mille Bornes is a really good low concentration game that works well with 2. We used to play it in college prior to going out while having a few beers with 20 minutes to kill.
Probably not engaging enough to be your go-to, but a nice palette cleanser.
Hnefatafl- It’s a board game played by the Vikings. Rules are simple. It’s fun to play. You’ll need to make a board. But you can use two colors of stones, with a specially marked stone for the king.
The game of chess started in India. It traveled to Europe, went through various changes and became the game we know. It also traveled to China and Japan.
Shogi is Japanese chess. You play on the intersections of lines (as in Go) rather than in squares. A captured piece may be put back on the board under your control.
Xianggi is Chinese chess. It has some important differences.
ETA Oops, I missed the word ‘contemporary’. I stand behind my recommendations though.
Two-player Risk is about as pointless as two-player Diplomacy IMO. Two-player Monopoly or Clue aren’t much better. You might try something like cribbage or Pente or maybe a two-player Avalon Hill game such as Panzerblitz.
Lots of good recommendations in this thread. I’ll hone in on two:
Twilight Struggle.
Twilight Struggle pits the US against the Soviet Union. Players take turns placing influence and activating events using card-driven mechanics. You can win by placing earning enough victory points, or by maneuvering your opponent into triggering nuclear war.
Learning Curve: Upper-Medium. This game is tricksy to learn, especially if you’re new to the very particular card-driven mechanics that the game uses. There are some nitpicky rules, and you’ll have to play a few times before you get all the rules down. Clever play depends on having good knowledge of all the cards in the deck.
Replayability: 7/10
A friend and I played this game probably 20 times in just a few weeks after I first bought this. Every game plays out differently, but within a historically defined structure. There are several different strategies that each side can use, and the game is all about reacting appropriately to what your enemy is doing and making constant adjustments to your overall strategy.
Theme: 10/10
If you’re into history, you’ll appreciate the amount of thought that went into the them here.
Mechanics: 8/10
The card-driven mechanic here is one that’s been used in a few other games by this company (most notably, Hannibal: Rome vs. Carthage). It creates a really nice feeling of head-to-head play combined with a need to make good decisions and justify opportunity costs. However, there are times that you’re going to be very frustrated by the system, especially when you end up backed into a corner about what cards you’re able to play.
Fun Factor: 9/10
This game has a lot of good stuff going on. It’s currently ranked on BoardGameGeek as the #1 war game, but it’s not really a war game. You’re not building armies or commanding troops, but there are lots of opportunities for you to go head-to-head against your opponent.
Overall: 9/10
This is a very adversarial game with several very clever mechanics. It has a strong historical theme, plays in a relatively short period of time, and is also rather nice-looking. Make sure you get the deluxe edition, which comes with a better board and some slight rules tweaks. Probably my best board game purchase of 2012.
Hammer of the Scots
Overview:
This game was directly inspired by the movie Braveheart, when a bunch of board game nerds said, “what if we make a fairly accurate boardgame about William Wallace?” Hammer of the Scots uses a system wherein your troops are represented by small wooden blocks that stand upright so that only you can see the specifics of your troops. Your opponent only gets to see your stuff when you sit down and fight. One player is England, one player is Scotland. The goal is to control the most areas by the end of the game.
Learning Curve: Medium-High
It’s going to take you a while to learn this game. There are some niggly rules, just like the above game. The good news is that if you like it, there are a lot of really excellent games that use the same combat system, including one called Crusader Rex, which takes place during the third crusade.
Replayability: 10/10.
Lots of strategies to try and a certain amount of randomness make every game play out differently.
Theme: 10/10
Scotland and England both have strengths and weaknesses that play out nicely in this game.
Mechanics: 9/10
This is definitely a wargame, and a good one for newer players since the scope is fairly small. Once you get the rules down, the way each turn plays out is fairly straightforward, and
there’s not much room for confusion.
Fun Factor: 10/10
My favorite game of all time, though partially out of nostalgia value. Games can take a few hours, though you can easily set all the pieces face down and leave pick up later on.
Overall: 10/10
A great pick. High quality pieces, well-defined sides, interesting battle mechanics. England is big and beefy, but slow. Scotland has weaker troops but more versatility and speed. Dice-driven combat give the opportunity to take big risks for big rewards.
Unrelated to both of these, there are a few alternate versions of Axis and Allies designed for two players specifically. Axis and Allies: D-Day is pretty decent.
This might have just been a joke that whooshed me, but just to make sure: she was passing you the China card after she played it, right? She can’t have played it more than twice more than you.
Some quick thoughts:
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Twilight Struggle is a great game, but it rather advanced as games go. I wouldn’t really compare it to RISK. There is a world map of connected countries, but the similarities end there. The mechanics are all very different. There is significant advantage in knowing what cards are coming and what they do, so the more you play, the more subtle the strategy optimizations can get. If you two aren’t the type to dive deep into decision trees, probabilities, etc., the game probably won’t amaze you, but simply be okay. If you are the type, then you should give it a crack for sure!
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RISK: Plays much better with more than two people.
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Settlers: Wouldn’t be great with two people. Negotiations and trading are important in the multiplayer game, and with the board so wide open with only two people, luck would be amplified and player interaction would be tremendously reduced.
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Stone Age: Plays well with 2, although I only got about five or six two-player games in before becoming somewhat bored with the 2-player dynamic, as the optimum 2-player strategy is (IMHO) easy to establish by then. Again, this depends on if you like playing games to pass the time in a social way or to have a mental challenge. If the former, Stone Age is a good one even past the sixth game. And if you ever think you’ll play with more than 2 players, it’s a good one to have on the shelf. Quick to explain and play.
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Tigris and Euphrates: Plays a little better with 3-4, but fine with 2. I haven’t played enough times to decide if the game is too luck-filled or not, but I’m still finding it interesting. Very unique game mechanics!
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Poker: Why not play some heads-up freeze-out tournaments? You each start with 50 chips and play 1/2-blind no-limit Texas hold’em until someone runs out of chips. Winner earns some pre-determined amount from the loser. Can be just $5 if that fits the bill. (Remember: in heads-up play, the dealer is the small blind!)
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Dominion: A very good deck-building game that is quick to learn. Plays great with two players if you are okay with minimal interaction. Unless the random selection of ten cards in-play have attacks in them and someone also chooses to play a strategy that includes those cards, the only interaction is in end-game timing (when to take the last card(s) that will trigger the end game). I’m okay with minimal interaction since the game is fast and the “interaction” comes in at the meta level of seeing who came up with the best line of play for the board or who executed it the best. Get an expansion set or two if you like the game to add more variety to the viable strategies.
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Citadels: In the interest of full disclosure, I don’t like this game much anymore. But I enjoyed it the first 5 to 7 times I played it. In the two-player dynamic, it gets pretty routine after a few games. In the 4+ player dynamic, there is too much deadtime (since you can’t think about your next turn at all while others are going).
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Agricola: Fantastic game, plays very well two-player. Lots of re-playability due to a large deck of cards, of which only a handful are in play during each game to perturb your strategy.
I opened this thread to recommend backgammon only to see the OP already covered it. But honestly, it’s probably my favorite two-person game.
So then I was going to suggest Go until I got to this post.
Another advantage to Go is that it’s quite easy to handicap by starting one player off with a number of stones already placed on the board in designated locations. More stones = greater handicap. It’s a beautiful game.
My wife and I play Carcasonne and Mr. Jack in New York fairly regularly. Carcasonne is a pretty easy to learn game and lighter fare than some other games mentioned here. It’s a great gateway game from Risk and similar common board games to hobby games. Each turn, a player places a tile to create fields, cities, and roads, then they may play a worker. Completing features with your workers scores you points. High score when the tiles are exhausted wins.
Mr. Jack in New York is a detective game. One player is Mr. Jack, the other is the detective. Mr. Jack tries to escape Manhattan or elude the detective for 8 turns while the detective tries to determine who Mr. Jack is and apprehend him. This one is a real brain burner and takes a few plays to get the hang of.
I like co-op games like Pandemic and Arkham Horror. Of the two, Pandemic is very much the lighter of the two, but even that’s too fiddley for my wife. Either plays well with 2 people, though I’d certainly play more than one character per person in Arkham.
The already mentioned Catan and Dominion are good. Both are good gateway games. Dominion is fast to learn but a very deep game. I’ve been on the receiving ends of severe thrashings where I don’t understand what I did wrong, and I’ve given a few of them as well. I learned Innovation a week ago and liked it.
Glory to Rome and Race for the Galaxy are two games with a lot in common that play well with two. Of the two, I prefer Glory to Rome, which I think also has the easier learning curve if only because of the damn symbology in Race. Both are card games with reasonable prices, to the barrier to entry is lower than Arkham Horror and other games with lots of pieces.
It’s a 2-4 player competitive strategy game. It’s a lot of fun and the games don’t last too long (around 30 minutes). A friend likened it to chess. You pick a faction, which determines the units you get, and you take turns drawing units at random and placing them on the map. When the map is full, or a player plays a battle card, all units execute their attacks in a specified order (determined by the unit’s initiative). The goal is to destroy, your opponent’s headquarters. End game occurs when only one player remains or when one player has drawn all their units.
It’s also available on Android for $2 (and maybe iOS?); it’s great if you have a tablet. If you have a smartphone and aren’t sure you want to commit to the full price, you could always buy the app and see if you like it.
Dominion is my number one recommendation for this, because its replayability is so high. I also like Lost Cities quite a bit.
I wouldn’t really recommend it in this situation, since he’s looking for a game to play with one other person. Dominion is dramatically improved by having four (or even three) players.
It is a truly excellent game, though, and wouldn’t be a bad purchase.
Wow! Thanks for the in depth replies.
We’re leaning towards Pandemic to start off with since it’s cooperative and we’re both hooked on Plague, Inc. 
Yes Pandemic is a good one.
Let me add Power Grid Like Pandemic is not just for 2 players but you can still really enjoy it when there are 2 of you. It’s not cooperative though.
I’ll second both of these!
Another shout out for mancala. It is really simple to learn, but can be devilishly addictive.