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Posted by http://www.cs.northwestern.edu/~hunicke/MDA.pdf
Personally, I recommend the MDA (Mechanics, Dynamics, Aesthetics) approach and looking at the 8 Aesthetics( Main Reasons why people play games):
1. Sensation
Game as sense-pleasure (Hearing/music - Catherine, Sight/art - El Shaddai )
2. Fantasy
as make-believe (Soldier - Call of Duty, Spy - Splinter Cell, Mage/Warrior/Rogue - Skyrim, etc, etc)
3. Narrative
Game as drama (For the story, Most J-RPG's, Spec Ops: The Line, etc)
4. Challenge
Game as obstacle course (Super Meat Boy, Demons Souls, Any game that's hard)
5. Fellowship
Game as social framework (Teamwork with other people. Horde on Gears of War, Co-op mode on any game, etc)
6. Discovery
Game as uncharted territory (Wandering around Skyrim, Fallout 3, Sandbox games)
7. Expression
Game as self-discovery (Allow's a person to express themselves. Through choices, in-game creation - minecraft, music creation in Mabinogi, etc)
8. Submission
Game as pastime (To lose oneself in, mindless past-time. Pokemon, Final Fantasy, etc)
Personally, I have one more:
9. Competition
Game as competition (Multiplayer in Call of Duty)
These are the reasons people play games.
Most games have at least three aesthetics. Although some games have fragments of other aesthetics, Mario having story to rescue princess, nobody plays Mario for the story, thus Narrative isn't an aesthetic in Mario.