FORENOTE: This post is somewhat system-neutral. I put it here because I play lots of 3.x, and my mechanic-heavy tendencies have driven some of my friends away.
Ahem.
I am an optimizer at heart. I think it's genetic. (My uncle is an optimizer too!)
To me, some of the greatest thrills come with the assurance that I've made the best character possible to fit my goals within the scope of the rules. I've cringed because I played a character and saw an optimization mistake I couldn't fix.
My background may have something to do with it. I was the prime bullying victim for many years of my life. I was largely a reclusive intellectual. The story is long and complicated, so I'll skip to the point: I found games, especially 3.x, to be a way to secure lots of power for myself. Sure, it's game power, but something good is better than nothing good, eh?
Of course, my tendency toward optimization flourished. I've played enough of Battletoads and hard games like it to know that optimization = survival, and, well, I want to live. (Dead people rarely win.)
With great power comes great responsibility. I played a Hood cohort in Red Hand of Doom. Nothing printed in that module lasted a single round, if I hit twice. Nothing! After that, I focused on support characters, but mostly Wizards. I was the party savior, a role I came to enjoy. I did grow tire of it, because we kept playing the same first 6 or so levels, and my options and tactics were largely the same. (Being a grappling Wizard helps a bit. Enemies never see it coming!)
Though I founded my current D&D group, I'm the person who cares most about the mechanics. Others care more for story. I care for story as well, and loved how engaging Dragon Age: Origins (PC) was. Still, too often, I'm told to ignore mechanics for the sake of story. For me, mechanics should be the basis of the story. (I know there are plenty of exceptions that exist and that should exist for the sake of plot, but being quietly told over and over to ignore my sensibilities and 'just have fun' or 'just roll with it' irks me.)
For me, this comes to the fundamental point of the game. I want a playground. I own seventy 3.x books at last count, and I want to use them! Story is important, but this is ultimately a game where characters are more important than plot, and what the PCs and their players do and can do are more important than the world, its locations, and its NPCs. I suspect this revelation is why I'm posting this mechanics rant here now instead of playing another game. (And why I'm hoping SirPercival will update on my solo PBP game soon. Man, that's thrilling!)