Depends on the game, really. What I want most from a turn-based strategy game (that would be "strategy") isn't what I want most from a simulation or pure shooter, etc.
If I had to pick one general form of gameplay that appeals most to me, though, I'd have to go with something that didn't appear to be one of the poll options: exploration.
The related quality of immersiveness is pretty important to me, which encompasses things like appropriate graphics and ambient audio, significant depth of character interactions with the gameworld, as well as strongly-defined (and well-voiced) characters whose actions help to tell an intellectually and emotionally engaging story. The best games I've ever played have exercised not just my hands but my head and my heart as well.
But it's opportunities for exploration that I crave. Not merely exploration in the obvious sense of mapping physical terrain, but of discovering that which is unknown, of mapping the individual abstract rules of any system and perceiving their functional relationships.
What's around that corner? What's in that crate? What is that character's hidden motivation for helping me? Is there something useful hidden up in that tree? If I raise Slider X, what happens to Value Y over time? Is there a gorgeous visual panorama waiting for me if I turn left here instead of following the trail to the right? What happens if I combine essence of lotus with iguana bile and heat the mixture? Is there a pattern to those strange clicking sounds? What are the underlying rules that govern the crafting of armor? Is there some way to reach the top of that peak? How does magic work?
And so on. For me, it's not "how can I win as quickly as possible," but "how much of the gameworld can I experience and understand?"
The greatest game in the world -- from my perspective -- would combine the gameplay depth of System Shock/Deus Ex with the world-immersiveness of Oblivion/Fallout 3 and add the persistence and dynamism of online games. (Actually, having written that, I just realized I've already created a basic outline for what such a game might look like. Heh.
http://flatfingers-theory.blogspot.com/2008/06/living-world-massively-single-player.html)
I realize this kind of thing isn't everyone's cup of tea. Where's the visceral action? Where's the opportunity to demonstrate one's superiority to other players? Where's the community?
Those things are all valid ways of gaming. Done well, they're all aspects of good games, and I feel strongly that there ought to be plenty of games that reward those gameplay interests.
They're just not
my most preferred gameplay interest.
More exploration-oriented games, please. :)