An interesting note by Penny Arcade
 

Please go read the following newsposts by Tycho and Gabe, then please return.
http://www.penny-arcade.com/2007/12/03

Now... why do you play games?
Do you play games to say: "I played game x, and I beat it! I'm 1337! lol"
Or do you play games, so you can say: "I played game x, and I had fun playing it so far. I couldn't get past this point, but it's been a thrill all the way."

Me? I play games for fun, purely.
Sure, I'll brag about it if I beat this song on Guitar Hero with 5 stars, but I'll readily admit that you beating it on Expert is much more impressive than me on Medium.
It's all for fun for me.
For you?

In single player, I do it to have fun.

In multiplayer, I do it for teh epic lulz. There is no limit to the things I will do in a multiplayer game (digital or real life) to get the reactions that mark an epic win/fail.

I play both single player and multiplayer for fun, excet for fighting games. When I face a decent opponent, its personal.

Mostly for fun.
Though I like playing crazy difficult games for the challenge.
I still get out Silver Surfer every now and then when I think I may have some gaming skills developed. Every time I am wrong....so wrong....
I'll be crying in the corner now.

I think I play games for the chance to excel at them. So, I like hard games, but only if the challenge is in doing something precisely, not stuff like "lol random unkillable sniper!" This leads me to prefer platformers and rhythm games more than shooters. Oddly, I'm not big on fighting games, though they tend to be made with challenge in mind. I think it's my lack of competitiveness. Or just that I'm bad at them.

Anyway, I like "do it again, stupid" gameplay. I like levels that require memorization if they require it in order to come up with a strategy to beat them, not just because the elevator's going to randomly disappear or some equally cheap death.

I also like games that give me something to ooh and aww at. Not necessarily bloom lighting and such, more like an impressive world. I don't mind not being challenged if I'm forgetting that I'm a depressed college student for a while.

So, just for fun, a list of games I had in mind while writing this:

Challenge to excel: "Hell" in Cave Story, Stepmania, Guitar Hero, parts of Sonic and the Secret Rings, F-Zero.

Fighting games I suck at: Soul Calibur 2, Virtua Fighter, Tekken 3 (though, I dislike this game for the lack of relationship between how hard a move is to do and how much damage it does).

Games that distract me: Zelda, Animal Crossing, Metroid, all of Cave Story, Sonic 3 and Knuckles (not that this game is impressive, I've just played it so much and it's such a huge part of my childhood that I enter a trance-like state when playing it).

The story. I play games so I can see the story behind it, and get that feeling of accomplishment when I say, "I've done it."

I also play for the feeling of doing something cool, IE, kicking the shit out of the entire opposing team or performing some stylish maneuver. That was part of the reason I actually tolerated Matrix: Path of Neo. That and, you know, Jack Thompson making a guest appearance. Multiplay is my bitch.

I play usually for the story. I see games sort of like an interactive novel. Sure, it's fun now and then to bash, or get bashed by, my brothers in multiplayer, but that's not what I get the game for. Even co-op isn't as fun as just experiencing the game.

I play for beautiful fun fluidness and awesome mechanics. I love games that allow you to do things that are crazy and OH MY GOD worthy, like Line Rider and GTA, and most of the Mario games. Basically at the end of the day it was done for fun in playing and experiancing, not so much to be like "I beat this! yes!" Sometimes that's an added bonus, but it's not necessary.

I play Smash Bros. Melee with people a lot. Most of the time, I'm the winner, but there is this one boy who totally takes me apart, and when I play at cons, I don't usually take first (I took third twice, and I did take first when the prize was a DS Lite). I have more fun when I'm getting beaten if I'm not powerless the entire time, or they're playing with sportsmanship and not taking advantage of something to beat me.

Same here. If the game is lacking a story, I'll probably supply one with my own brain. I like to just play around on the games and imagine my own stories for what's going on.

Although, unlike what you said, I really enjoy co-op if it's done well (and I'm playing with the right people). There is nothing quite as fun as playing Four Swords with my three best friends.

I play multiplayer to crush my friends and see the poor look on anguish as I destroy their hopes and dreams.
Go competition!

Also, Star Wars Jedi Knight: Dark Forces 2 is the best multiplayer game ever. Jedi Academy sucked ass but we have this game pretty much perpetually running in our flat.