
I can and do literally spend hours upon hours customizing a character for a game before I even start playing it, whether it's my first time playing the game or not.
Another note on customization, I still love games where you are a character who has a story and a name, a pre-made look and little customization. However, I like as much as possible in these cases, but I do enjoy some good character humor once in awhile, where it's like your reading a book about the character you play and he says some great things you might not have expected.
#2 is story and character depth. I like a good story a lot, but more importantly I like a story that can move me. If it can make me laugh out loud, swear at the screen about an enemy or rival, shed tears, and make me miss my time with each and every one of the characters involved to an extent of feeling like I could no longer be with my friends any more when I'm through with the game, then it's a great story. A good reference, Legend of Dragoon. I remember being touched by the story in that game at the time I first played it, and also Dragon Warrior 7.
#3 Play-ability. I need to be able to play in a way that I enjoy, and also be able to play the game without frustration of bad game-mechanics, bugs, glitches, or generally anything that causes an unwanted negative interruption for me, due to the programming or graphics or some other technical conflict. This type of issue can very easily ruin what could have been a good or great game. By ruin, I mean kill.
#4 Graphics. An amazing looking game is great if it has the other things necessary to make it great, but as long as the game doesn't look like it was made for the Super Nintendo it's probably just fine.