Which Part of Game Do You Care About Most？

gameplay, graphics, story - in that order; for some genres, having local coop is also important
I don't care about MP or audio for most of the games (to be honest, I rarely play with sound)
PS: I added graphics because I completely avoid some graphics styles - for example, games that look like they were created with rpg-maker are on this list. There are however games I enjoyed, but they felt unpolished because of their graphics -. Fallen enchantress is one of them.

it's the whole package. it's stupid to say only graphics matter. and it's equally stupid to say only gameplay matters.

Gameplay and Control, and how its designed to use them in the game.

Atmosphere, graphics and gameplay all matter.
Something that doesn't matter is story/lore. I get all fidgety when some old dude starts telling me his life story... don't have the patience to get into a story when I'm just there to push some buttons. If I wanted a story, I'd read a book, which I never do anyway. I like story that's short, understandable without much effort, but still manages to be good somehow.

1. The main character.
2. Graphic
3. Soundtrack
4. Story
5. Control

performance, everything else is less important if game is lagging in few fps

all of them matters a good game is above descent in all those you mentioned plus sound you forgot the sound its important also , but tbh if a game is good in either story or gameplay alone it may survive but it will prob create a love club and hate club at the same time

Story, Gameplay, soundtrack and dialogues

1. The gameplay. It is a game afterall.
2. The graphics. It is a visual medium, so it has to be a style I don't dislike.
3. The atmosphere.
4. The story. I can count the number of games on one hand that had a decent story.

Totally depends what kind of game it is, for example Telltale games have bad gameplay, the graphics are ok, it's the opposite of complicated, but most have a good story and I'm fine with it that way.

Multiplayer games mostly have no story, good gameplay and some are more complicated, some less.

The most important thing for me is gameplay, I can't play games without good gameplay for a longer period of time and I can see past a rather bad story if the game is at least fun to play.

Graphics are the least important to me, it should just do its job.

It can be boring, that's all. If it's boring then neither graphics/gameplay/story/whatever will save it

So overall it comes to the point where basically the gameplay schemes are the most important

Depends on the game. I could play a game with somewhat crummy gameplay if the story is great, or I can play a game with a crummy story if the gampelay is great. I can play a game for the eye candy, or I can play a game that looks like this.

1. Gameplay (This includes controls and game feel)
2. Story (Only if it's a story driven game. Games like Overwatch, Rocket League, etc can be forgiven)
3. Music (Music can still make or break a game)
4. Graphics

Gameplay, atmosphere, design, controls, game mechanics, story, graphics, sound - in that particular order.

I care for all of those aspects, except for the multiplayer, I'm more of a single-player guy.
That said ,I can overlook flaws if the gameplay or story are good, and I prefer a good art-style over hyper realistic graphics.

I think I care the most about the simple enjoyement.
The game could be the best one ever created, but if I don't enjoy it, I won't play it.
On the other hand, if a game is average, or even below average, I'll stick with it as long as I'm having a good time.

Story is the second-most important to me.

The mechanics and gameplay. If the game "feels" good to play and there's depth within how I play it, nothing else matters.

The mechanics is generally what gets me into a game. After that it'd be story then presentation

All of the above, minus just shooting around. I do like co-op and the social side of some mmos

The gameplay is the most important part for me. If the gameplay isn't good, why should I play it?

The atmosphere and story.
I like Fallout 3 and New Vegas for atmosphere and the potential for justice in its sole discretion, which, unfortunately, impossible to do in real life.)

You have been on this site for over a month, and I would like to think that its not that hard to learn all the basic stuff.

Why did you categorize this as a puzzle if there is no puzzle?

Baldurs Gate's system isn't complex! Have powers, kill monsters. Maybe it can be a little "complex" with the lack of hand holding in terms of questing. It was a difficult game back in the day, but that was the norm!

If anything games now can be dumbed down making things like Baldurs Gate seem complex. Deep class systems and a wide variety of spells to pick from should be the norm within RPGs rather than cookie cutter "pick Rogue, have lockpick and bow" classes. /endrant

Gameplay + Story mainly

As obvious and ridiculous as it sounds, it needs to be fun :)