I like freedom in games. Freedom to go where I want and to interact with the world.
I haven't seen many non-linear action games. Most First Person Shooters actually remind me of the old arcade games like Operation Wolf. Shoot everything that moves, advance a bit, back to step one.
F.E.A.R., which I've been playing for a couple of days, is a good example of a bad game when it comes to freedom. Objects don't break when shot, not even a notebook on a table can be moved, and you can go only one way. A guy with weapons, grenades and inhuman powers can be stopped by a box on the other side of a closed door? It's also very repetitive, in my opinion.
Far Cry isn't really non-linear either, but at least there's some freedom to choose which way to go (except that the player can't climb to trees or steep hills, can't set the jungle to fire etc.).
In Half-Life 2 you can move and break many objects, and can even use them to go to places developers clearly haven't intended the player to go (you can avoid a couple of helicopters that way, and you can carry a turret to next level). Unfortunately it's also quite linear.
I can't comment about MMORPGs as I've only tried Guild Wars for a little, haven't even joined a guild.
I also like games that require thinking, such as those that have puzzles to solve. Just not those that require clicking on the correct pixel on the screen like in some old adventure games.
Oh, and good audio is always a big plus.
The thing that irritates me in many games is that there are too many enemies - and most of the time there are no peaceful people at all. Apparently I shouldn't want to explore the world but just kill everyone instead. Sometimes when there are peaceful people, they're rude (like in Morrowind, just standing still all the time but saying I'm busy).
And I've played too many games where the enemies have unlimited ammo and/or they appear from nowhere in neverending hordes.
At least in Tomb Raider games when you've shot all things that attacked you on the level, you're free to run around searching for secrets without someone popping up around the corner.
Driving games could be good, but most of the time if there are computer opponents, they all drive at the same speed and style regardless of what kind of a vehicle they're driving (a'la Need for Speed). Carmageddon series is a good exception, though.
NetHack still remains my favourite, except that there's no audio, and my pet eats corpses before I can sacrifice them or eat them myself. But at least I can use a fruit as a weapon, throw healing potions to monsters, dig through walls and floors, steal from shops, polymorph myself or others, read scrolls when drunk etc. That's what I call freedom in a game
