I play games mostly for entertainment purposes, whether it's the gameplay or other aspects that provide it depends on the genre. For example I don't care about shooting in games but some shooters are set in interesting and atmospheric worlds that I like to explore, in god mode. Unreal (1998) is a good example.

I play games for entertainment. I like to have fun and enjoy games I play, and to wind down for an hour before I go to sleep after a long day.
That said, I play variety of game types. Some I play because of gameplay (GTA, Resident Evil, Shadow of Mordor, Dying Light, the last Tomb Raider), some I play because of the story (Danganronpa, The Walking Dead, Bioshock Infinite, Metro, Spec Ops, Beyond 2 Souls), some I play because of the puzzles (Peggle, Tomb Raider/not the last one), some I play just for fun (sports games).

There is no predominant reason why I choose the game. All I know that the last thing I care about are graphics, sound even less -- and that I approach every game based on what it has to offer.

Then there are games I never play: Fighting games (too repetitive), racing games (too boring for me) and JRPGs (tried a few, made an attempt to like them, but I simply cannot embrace the turn-based gameplay).

I don't anymore.

Because it's fun. I find many types of games fun. There are periods where I hardly play anything at all for six months or more and then I play way too much for a few months but it is always about being entertained, challenged and enjoying myself.
I like good writing a whole lot and good game design is important but gameplay is very important as well; there are way too many pretty games that just aren't any fun at all.

Gameplay and the story.

Gameplay, then story. When it comes to RPGs is 50-50 tho

Graphics aren't on my list.

1. Gameplay
2. Story/Characters

I play games for so many reasons. Sometimes I play things strictly for the gameplay, things like racing games, shooters, sports, motion controlled, all of these I tend to play just for the joy of playing. Sometimes I play a game only because of the world it presents, in this case I don't really worry about gameplay. Then there are times when I play just for the sake of building up stats, in this case niether the story or the gameplay matter all that much. In rare occasions I play games to have a good time with others. In the rarest of occasions, I will hop online to compete with a friend, or just test my skills against other people.

There is no one reason why I play games. But, I guess the best way to narrow it down is. Games better than any other thing on the planet offer an extreamly wide range of experiences, mimiking nearly all aspects of real life, while taking you places nothing else can, and all at a price that my wallet can afford.

Wait, what? But, but.. why?

Because i play games.