1)Story
2)Music
3)Graphics-Particularly ART STYLE
4)Controls
5)World Design
A story is the major part of the game to me, I didn't like FFX for the story, don't get me wrong, it's an okay game, but the story was just bad. Freedom Wars doesn't have a good story, but it motivates you to keep playing, Golden Sun-Dark Dawn, now that is a truly good story, It may be long but the story keeps you in the game.
Music, I play the Cello, and I can tell you, there are times were you play a song that you just absolutely hate because of how uneventful it is. If the music is interesting (Not counting Rhythm games) and eventful, and if the music MATCHES what is going on, like an epic boss battle with heavy music and interest as you only hear it once. I'm just a Music buff, okay, I know.
Graphics- If the art style is interesting like Okami or Assassins Creed Black Flag. If it matches the style of music as well, such as a dark place with eerie music, games like Final Fantasy Chronicles perfects this to me. Freedom Wars as well.
Controls- I'm not fully pissed when they get this wrong, all I do is adapt, but Other M is awkward, that is just bad controls. Freedom Wars has a beautiful control system. It's free moving in a sense.
World Design- Games like Freedom Wars don't need a good world design because of the type of game they are, but a game like Final Fantasy Chronicels or Bravely Default NEED that world design, but I'm not big on this.
EXTRA! Puzzles- I like puzzles, Metroid and Golden Sun Dark Dawn, are full of puzzles, and I just love puzzles! XD