I appreciate both together or separate. Super Mario games say it all. When a game is gameplay heavy with little to no story then it's good to pass the time and have fun or maybe just make you feel like a badass depending on the game. Gameplay is also an important part to gaming. What good is a game if the gameplay isn't appealing or good at all? It just makes you feel like the story was going somewhere but you weren't to motivated to continue the game for just a story. Sorta like the game Heavy Rain, depending if you enjoy that type of thing. Now a gamer like me can really appreciate a story heavy game with characters that make you feel something with great-unique gameplay. Both elements together is what makes me a gamer even though I can still enjoy a good gameplay based game (Maybe gameplay more then story) or a story driven game at times.
I like both, but the gameplay is the most important part. Even if you have the greatest story ever written, if the game itself is crap, the story seems like crap. That's why I'm not that big on the Zelda "timeline" thing.
I prefer gameplay over story. Mainly because they're games, not books, not movies, games. What makes games different from books and movies? Gameplay. Don't get me wrong, a good story in a game isn't unwelcome, but unless it has gameplay that's fun, I'll probably wind up stopping before I'm done with the game. However, if a game's got no story at all but good enough gameplay, chances are I won't stop before I'm done with it. In fact, I tend to prefer more gameplay based games because I hate seeing a ton of cutscenes that last forever, just to get back to the game, walk a few more steps, and learn that cutscenes are almost like random battles. Of course, not all of them are like that, it's more of an example.
But really, I just prefer gameplay. I'd rather play a game I have fun actually playing than one that feels more like a movie. If I wanted that I'd probably, y'know, watch a movie. Or probably not, because I'd prefer a game any day regardless of which condition it fulfilled.
Depends on the subject matter I suppose... a lot of older games were less story driven but still maintained incredible playability. Mario and Sonic games, for example. There is some narrative going on, albeit very little, but this is made up for by being fun and enjoyable to play.
I, however, love games that tell an interesting story. I consider them to be an interactive movie, of sorts. And I've played my way through some awful games just because I wanted to know how the story turned out. I've also given up on games that have too complicated a story, so there is definitely a very fine balance.
Story-driven for sure. Looking back, most of the games I've enjoyed most were the story-centric ones, like the Metal Gear Solid series and Mafia series. The gameplay has to be decent too though, there are many games out there that have good stories but are unplayable because of the gameplay.
I'm more into story driven games. Which is why I enjoy Zelda games so much: I personally believe that this series has the best plots of any video games. Particularly Twilight Princess. The story for that game have very profound and in-depth, and that is mostly the reason I like the game so much. Now I do pay attention to the gameplay value of the games also, as gameplay probably is what makes a game fun to play in the first place.