I've tried a bunch of stuff... I tried Monkey Island and she thought it was boring. I tried Machinarium and she thought it was too hard to be fun. I tried shooters and she kind of got a kick out of running around shooting people for a bit, but then got bored when there were story elements. She asked me to play Fallout New Vegas because she knows the series is my favorite, but she got bored of all the talking and me trying to explain the stat elements.
I want her to try Amnesia soon, since it is relatively simple and she likes scary movies. She also loved watching me play Mirror's Edge because of the music and style, so I might have her give that a go herself at some point.
I "tried" a lot of games with my girlfriend, and many of them bored her to death.
Here is the list of games she actually likes (beware - there is a VERY surprising one)
Zuma (free) clones
Plants vs Zombies "Uhhh cutie plants ! Look at the marigold there ! Oh, the nice little mushroom" - (since I bought the game, I halved my time of play because she captured the computer)
King's Bounty "oh... squirrel ! Oh ! I want animals in my army ! Cute snakes"
Civilisation IV "Oh... now I am going to build a theater... and after Public Bath"
An (outstanding) brownser game called "Hordes", now in English ("Die2Nite") because you get to talk to people from all over France / Quebec / Belgium (now : the World).
S.T.A.L.K.E.R. Call of Pryapiat "Ohhh.... This building ... we had it in Romania as well back then..." "Oh... funny accent guy again".