Nice ones Hadrian, knew I'd forgotten something.
Whether an mmofps or not, I want a persistent avatar I choose. Unlocks you get from leveling up can be better looking gear.
I like partially destruct able environments. I don't want everything destroyable because then you just end up playing in rubble. But areas you can blow to grant extra ways around the map if you kit yourself out for it (again, something you can level up to unlock the abilities of demolitions).