I started playing October 2009, if my timestamps in that folder are to be believed. I'd heard about it before then from the now-defunct Computer Games Magazine (I miss that mag.) It had a bunch of free games in it, and I was playing through them since I'm a cheap bastard and didn't have the scratch to upgrade my system to accommodate newer games.
I don't really remember my first fort apart from completely failing to understand z-lvls and soil layers- I was playing out of the wiki at that point (and I still am, to be honest) and was following the Your First Fort Guide; for the life of me I couldn't figure out how to dig, since I thought the unmined rock was only the black space- I didn't realize my designations had to cover the borders to give my dorfs access.
What really stands out in my memory is my first true fort, where it suddenly clicked. I'm as stubborn as I am cheap, so I'd been plugging away at this game for about four hours, and suddenly it MADE SENSE. I could see the grass, and the walls, and the trees and the hills. I knew what tiles were significant and which I could safely ignore. It was a feeling I hadn't had since I was 8 years old playing Age of Empires for the first time, when I didn't understand the concept of a tutorial. A big part of what got me into the game (and keeps me coming back) is the sense of discovery, of learning new things about the world, especially since those new things are internally consistent and predictable- rather like a particularly clever riddle.
My first true fort fell not to starvation, or goblins, or tantrums, but to sturgeons. This was back in 40d, and my dwarves would chop down the willows by the river and then the haulers would get dragged in by the fish. After I lost half my dwarves before I figured out what was going on, I abandoned and went on to make a new fort with my newfound understanding of the game. I played more or less constantly for almost a year, and every month or so I'll go on another binge when I get the urge to build, or when a new release promises new features.