Typically, I enjoy diversity with my games. Due in no small part to my ADHD, I feel an insatiable urge to keep myself entertained, and my short attention span ensures that if I have to repeat a task for longer than 15-30 minutes, I'll typically get bored of it and try to "entertain" myself while being entertained, i.e. watch a movie while playing a game. So, more than anything, I hate games that have you doing the same thing for long periods of time. The definition of "same thing" is rather vague, though, as even just killing different monsters can keep my attention...for a while, at least.
No, a game that can truly appease me is one that has a lot of stuff to do. Side-quests, secret dungeons, and most importantly, mini-games. I see fewer and fewer video games with mini-games nowadays. For whatever reason, though, sandbox games kind of go too far for me, as when you give me TOO MUCH stuff to do, I end up forgetting what the main story was and lose immersion on an epic scale (for no better example of this, look to FFXII and their god-awfully long monster hunting sidequest, not to mention all the other things you can do). I enjoy a fair balance between linearity and free-roaming, but I don't think I've ever nailed down a proper formula.
Besides that, I'm a big fantasy fan. I love Dragons, Swords and Sorcery, "Dated" settings and awe-inspiring worlds. I'm not a big fan of much else, though; Sci-fi is very hit-and-miss with me, though I've found Steampunk to be rather nice on occasion. Oh, and I HATE realism, and I ESPECIALLY hate bland colors. I absolutely LOVE bright, colorful regions and unbelievable scenery; doesn't matter what you put in them, as long as I can see every color of the rainbow, with nothing toned down to look "serious," I'm happy.
Everything else becomes less a factor of buy or pass and more a factor of how well I enjoyed myself. Music is always a factor in determining a good game from a great game, but I have no real preferences as to what I want to hear; as long as it sets the mood, I'm happy. Story is also a big factor, but I'm pretty good at reading between the lines and crafting my own ideas about the world I'm in; though, quite frankly, any game that has me going through 10-15 minutes of not just written, but SPOKEN dialogue just makes me want to take a bullet to my brain out of boredom every time.