Another vote for Carcassonne. MrWhatsit and I play it all the time, and it really never gets old.
If you want to get rid of your partner, invest in some old Avalon Hill games (War at Sea, Victory in the Pacific*, D-Day, etc. etc.) and insist that they have as good a grasp of the rules as you do (and you can make up a few on the fly! It will take hours of research to discover the ploy!) or, if they refuse, make them be the Axis powers at the begining of the game (“But honey, look how many more troops/ships/territory you have! How could you lose? I’ll be lucky to not get wipped out after the first turn!”).
Guarentee you to be single and hitting the “Meet and Meat” scene in no time! 
*Actually a pretty easy game, but we could never really get a grasp on the whole “patrol” issue. The “day vs. night” action always led to strife and accusations of “bogus dice rolling”. And no matter how well the Japanese side does at the begining, they were pretty much always doomed to fail once the American replacements ramped up.
The Farming Game - wonderful game.
I’m agreed on Fluxx. Just remember to remove the Reverse Order card if you’re only playing two player, as it’s a dead draw.
Another superb card game is Guillotine, though you may find it hard to get hold of these days.
I own and play a lot of board games. My current inventory, give or take a title, is at www.abunchof.us (along with some other things, though it is still under construction. Some good suggestions have been given, but let me add a few more:
Carcassonne - the game gets more beautiful as each tile is laid and plays equally well for 2-4 players. Keep an eye open for Carcassonne:the Castle which is specifically two player and is a fantastic game as well.
Balloon Cup - this was designed by a close friend of mine, Stephen ‘Snoop’ Glenn. Balloons are either in valleys or mountains. High total of cards wins on mountains, low wins in valleys. Each turn you can play one card to either your side OR your opponent’s side. I am really bad at it, but still thoroughly enjoy it.
Clans - plays 2-4. The game is similar to Nim in gameplay, but there is also an element of deduction because whenever a single group is formed, the members of that group score points. Based on this, you try to deduce what color your opponent is (the colors are dealt secretly before the game) so that you can prevent them from scoring again.
Yinsh - I nearly forgot this game. It is part of the GIPF series of two player games, and in my opinion, the best (although Dvonn is also strong). It combines elements of tic tac toe with Othello, and has a great balancing factor so that a player in the lead is slightly handicapped. REALLY like this game, but do not get to play it enough.
Battle Line - I actually own the game this was based on, Schotten-Totten (which is out of print). Similar to Balloon Cup, but you can onlly play to your side, and the best three-card poker hand wins territory. You want to win either three territories in a row, or five of the nine, to win the game.
Attika - One of my favorite games of recent release. You try to play all of your buildings in the ever-growing province of Attika, OR you try to connect two of the oracles with your buildings, while at the same time stopping your opponent. Another game that plays very well with 2-4. Because the initial board changes with each new game, it remains fresh as well.
Alhambra - Last year’s winner of Spiel De Jehres (game of the year). On your turn you either pick up money or use money to buy a building. If you buy a building with exact change, you get another turn. The buildings form together to build a small palace area with walls running every which way. Points are scored at various points for majorities in building types as well as wall lengths. The game plays for 6, but to me it is too chaotic with anything above 4, but is great for 2 as well.
There are usually plenty of photos and other reviews of these titles at www.boardgamegeek.com to see if anything appeals to you.
If you can find a copy, second hand maybe, I would recommend **Raiders and Traders ** - nice game of ancient Greece and not too wargamey.
Someone has mentioned it before I would strongly recommend **Board Game Geeks ** website - by gamers for gamers with reviews, recommendations, scores, search functions. Very good to find what might appeal.
What is it about role-playing that she doesn’t like? Is it the geek factor? The elves and dwarves and fantasy trappings? My wife **Dangerosa ** is not fond of role-playing for the most part, but has played and enjoyed some games, and likes computer RPGs just fine. I’m not sure if you have a strong hankerin’ for them, but if you do, you might try some experimentation and see if you can find something she likes.
Also, have you considered options such as a game system? We have a PS2, and both of us really enjoy the SSX series of snowboarding games. Those can be played together or one can play while the other just watches (which is pretty amazing, by the way – it’s a great-looking game). No geeky role-playing at all.
There’s also the Eye Toy, which is a great get-up-and-move attachment. It comes with 12 games (the PLAY version does, at least), which are loads of fun for all ages. My kids (ages 4 and 5) think they’re a blast, and I find them fun and kind of challenging as well.
And there’s Dance Dance Revolution, which I have not played but I am informed is the bee’s knees. Or something.
I got to throw my bones in with Acquire and Axis & Allies.
Acquire is a business simulator that uses tiles on a board to represent companies. Its a VERY simple game to learn (about an hour or so) and has an almost infinite replayability. The wife and I play this about three times a week with just the two of us, and once a week with a group of six (which is SUPER CRAZY FUN!!!111).
Axis & Allies is another classic game, also by Avalon Hill based on World War II. While most ‘chicks’ ( ) don’t dig military based games, the missus really enjoys it due to the strategic elements.
I’m assuming you and the missus are looking for a nice game the two of you may play after dinner and before bed.
I would second the suggestion of Sequence. A round can be played in as little as 30 minutes, and it make you think.
I would also suggset Master Mind. This has the added advantage that it is (mostly) portable. It is also a thinking game.
I would really like to recommend Gipf and Dvonn from the set of games in the link. I haven’t had a chance to play any of the others, but these two are really neat (I like Dvonn better, though).
I used to have a set of sheets with the pattern of a Backgamon board imprinted on them. My girlfriend of the time and I used to use “playing Backgamon” as a convenient euphemism for the games we really played on them…
Looks like I’m late to the party, but I’ll chime in anyway.
Carcassonne was the first game to jump to my mind too. It is all it’s cracked up to be, and more. The Castle is fun too, but the original works fine for 2 players, and expands up to 5 (6 with the Inns & Cathedrals expansion) for when you’ve got other folk around.
I have no clue how Settlers is similar to an RPG, but as mentioned, it’s 3 players and up. Since it’s a trading game, I can’t imagine how boring it would be for two. The Card game version works for 2, but it’s nowhere near as good as the original. So, as much as it pains me to say this about such a great game, if it’s just the two of you, skip Settlers.
Other good ideas that have cropped up so far: Dvonn, Othello, Stratego,Eurorails,Hera & Zeus,Ceasar & Cleopatra, & Alhambra.
If you’ve still got the Go board, you can try Omok. Simply take turns putting a piece on the board and try to get 5 in a row (up, down, or diagonally). The only other rule is you can’t make a “3-3” (i.e. two unblocked 3 in a rows that force our opponent to block one of them, giving you an unblockable 4 in a row.)
Ice Towers has been mentioned, but you might want to buy it as Zendo which is a very fun logic game using the same pieces that my fiancee and I can’t get enough of.
If you’re having trouble deciding, or finding these games, www.funagain.com and www.bouldergames.com are two good places to browse around reading reviews and such, and also have very good prices.
The Awful Green Things From Outer Space is a great two-person board game. It’s an assymmetric game (different rules for each player) that’s fairly well balanced. Lots of fun…
There is also Knightmare Chess, which combines a card-based game with chess. Interesting, if you like chess but want some variety.
I really like Quoridor.
If you’re looking for very simple yet rather deep, take a look-see at this book.
If those fail, I’d recommend Don’t Whiz on the Electric Fence!
Just to quibble a bit, but I don’t think TAGTFOS is well-balanced – at least from the last time I played it, the Awful Green Things player had a distinct advantage over the other player, who was often left trying stuff at random and hoping to get a working weapon soon enough. Fun game, but not quite a 50-50 contest IMO.
As for suggestions, Parker Bros. had Clue: The Museum Caper a while ago. Dunno if it’s still available, but it’s a fun thinking game that’s fairly fast to play, and works well for two players.
Carcassonne is okay for two, but Carcassonne: The Castle is great two-player fun.
Through the Desert is an excellent abstract strategy game that plays equally well for 2-5 players.
I’m not sure about Viking chess, but The Viking Game is a commercial version of a historical game known variously as Hnefatafl or Tafl or Tablut. You can Google for rules and more information. I made my own hnefi set very inexpensively.
If either of you are Discworld fans, you may be interested in Thud. Or even if you’re not, it’s a fine strategy game. It looks a lot like hnefatafl, but the play is very different.
Others have mentioned games played with Icehouse pieces. I’ll add Ice Chess (formerly Pikemen) and Martian Chess, both of which can be played with just two stashes, unlike Ice Towers and Zendo. Aquarius is okay for two players, too, and if you get two decks you can play Pantopia.
And cribbage and backgammon, of course, rock.
Here is a place that has loads of great games that won’t bankrupt you.
One of my favorites is Devil Bunny Needs a Ham.
I’ll put in another vote for Cribbage. I love it.
Trivial Pursuit can be fun with two, if you tweak the rules a little.
There is a fast paced card game called Blink that Ardred and I have fun with.
Why? We always play it as a “take another turn” card when it goes down, and as a “take another turn” card when it goes away, and have no problem with it. Fluxx is a great game, but it playability is not huge, IMO: it’s mostly good for breaking out at parties.
burundi and i play lots of cribbage and lots of Boggle.
Daniel
My immediate answer would be that it’s easier to ditch it than to create a house rule. Besides, playing it your way can give someone three turns in a row if they can also play Rules Reset, Let’s Simplify or Trash A New Rule - that’s just too good.