Via Slashdot, I stumbled upon several articles answering that question. So here's my answer.
I started using Linux in mid-2003. I had received $2000 to build a computer for Christmas 2002 (and nothing else, either for Christmas or my birthday, that year) as I was at the point in high school where I really needed one and interested in learning how to put my own together. Knowing that I could spend an extra $100 on slightly better hardware if I didn't pay for Windows 2000, I obtained a copy from a friend… yes, illegally. Convinced over a six-month period that Windows 2000 was too much work, and that it was probably a good idea to go along with existing copyright law whether I thought it was good or not, I started to seek alternatives. A classmate gave me a copy of Slackware, but text-based installation was a little intimidating. Finally, a friend who was a Linux administrator at the local community college gave me SuSE 8.1… and it was great! Now, by great I mean it worked, and I embarked on the long quest to figure out how to do all the things I was using Windows for. I had already been using Firefox, Thunderbird, and OpenOffice, so that was easy enough, but what about the games??? No dice. Wine? Needs 3D acceleration. That means getting graphics card drivers… and I had a Radeon. Not an auspicious start, as those of you with ATI cards probably know, but after months of fiddling with it and getting deep into the command line, my interest shifted. The rest is history. When Novell bought SuSE, I bought Fedora 4 Unleashed and switched distros. I've used SuSE 8.1, 8.2, and 9.0; Slackware 11.0, and Fedora 4, 6, 7, 9, and 10. Can't wait for 11!
What did you do first with Linux?