Theme is the most important to me, but it's not as simple as the genre examples given in the poll. There is just as much unappealing fantasy and science fiction as there is fsf that looks really cool to me. I avoid horror as a genre, but that's the only case where I avoid a whole genre like that. As far as archetypes go, I've played pretty much all of them at one time or another. There are several I don't usually play (like a racing game or a sports game) that I would play if the theme was particularly interesting (racing animals instead of cars, playing a fantasy sport involving magic). On the other hand I'll usually start my search for a new game by deciding what gameplay archetype I'm in the mood for (like MMO, time management, tactical RPG...) and I'll look within that archetype at the specific gameplay features and theme/story of individual games to see if there's something that makes the game look more or less appealing than average for the gameplay archetype.
Edit: Oh, people above are considering story to be separate from theme? Normally I consider theme to be the abstract high-level part of story. But I can agree with choosing games based on story, if it's an archetype that has story. Or for that matter with being put off by the story even if the archetype is good. (I love Skyrim's gameplay, but the story is really not my cup of tea; I'd love to see the same gameplay with a different story.)