Posting on behalf of my wife who doesn't have an account here:
A few years back when I told my wife I wanted to get a PS3, she looked over the selection of available games at the time and had no interest in any of them. She was pining for the Mario and Zelda games she had played years ago. So, we actually got a PS3 and a GameCube the same week.
At first she spent most of her time on the GameCube going through Windwaker and Twilight Princess (multiple playthroughs of each). She also loved Prince of Persia: Sands of Time. To a lesser extent she played some of the other Zelda and Prince of Persia games plus Super Mario Sunshine, but didn't enjoy any of those as much as the first three.
One of the first games I got for the PS3 was Elder Scrolls 4: Oblivion. After seeing me play it for a while she gave it a try and ended up finishing all of the main storylines before me. Same with Fallout 3 and Dragon Age: Origins where she finished all of the DLCs before I started any of them. So, she's definitely into action-oriented RPGs and is looking forward to Dragon Age 2 and Elder Scrolls 5 (if less buggy than 4).
She also loves the genre of "platformy action games with hidden treasure and killing" (for lack of a better term), having gone through the Prince of Persia reboot, all three of the Assassin's Creed games, Drake's Fortune, and all three God of War games. Currently she's midway through the PS3 re-release of the Sly Collection.
Batman: Arkham Asylum, Bioshock 1 & 2, and Civilization: Revolution round out the majority of her PS3 experience so far.
That's what she likes. What she doesn't like, or at least hasn't taken any interest in from seeing me play them, are open world non-RPGs (GTA IV, Red Dead Redemption), FPS or third-person shooters (Resistance, Rainbow Six Vegas 2, Call of Duty 4), or anything to do with driving, which she hates in real life too (Motorstorm and GTA IV again).
In general, what she likes in a game is character progression (leveling up, choosing new attributes, etc.), beating a tough boss, puzzle solving, and finding every last hidden item. She'll replay a games several times as different character classes or with different approaches if there's enough variety to keep it from getting tedious.
What we'd both like to see more of, or any of for that matter, is games with good two-player co-op mode so that we can stop racing to be the first to grab the controller.