Depends on the genre really. For action/action-adventure/rpg games in general, it's by far the combat mechanics/battle system. I can't point my finger on my favorite aspect of shooters though. The atmosphere and soundtrack can also greatly increase my enjoyment, and so can the visuals - both on a technical level or with an interesting art style (e.g. Okami).

Story is the thing I value the least. I can easily go back to a game with a terrible story and great gameplay, but not the other way around - Grandia 3 is one of my favorite rpgs, and the plot is really silly, for example. I see the plot as nice bonus rather than a requirement.

gamepmusic

gameplay.

1. Atmosphere
2. Characters
3. Story
4. Gameplay
5. Graphics
6. Music

...

1,000,000. DLC

Resolution and Frames Per Second. Since that seems to be the defining factor of a good game this generation /s

Seriously though, It's probably good characters and accessible gameplay.

Great gameplay and even greater level / game design. There's nothing worse than playing a game that looks and sounds pretty but feels hollow because of poor / repetitive gameplay mechanics and uninspired design.

720p/59fps

Jiggle Physics
Tits
Story
Gameplay

In that order btw

Story/Gameplay

Fun