It depends...
On an rpg I want story, On a shooter I want controlls I want in game voice chat, and i want fast gameplay, something like counterstrike where if you mess up in a rush and are the first one to get killed you have to wait 30 minutes to play again I am not satisfied because i play a shooter to feel the adrenaline, not watch other people.
If I'm playing a mmo or mso i want supreme customization, this is why I dont play mmo's they claim to have customization but they really dont, in the end game everyone is wearing the same stuff... Same goes for mso (massively single player) if i am playing something like oblivion I need thoose mods with 80 billion extra weapons so that the game doesnt get dull as soon as i get full daedric with reflect damage and spells...
In an RTS I need controls, this is why I chose starcraft over C&C any day, starcraft is nice and simple to understand and relies more on strategy and microing as a RTS should.
And all games I play must be open to modification or are just total BA classics like Sukoden 1 for the ps1