What got me started was the suggestion by a local shop guy who's been into it since long before they were cool. I was fairly new back to road biking after a long break, and I was riding a vintage Italian bike. I decided to just try going for a ride, leaving it in one gear and pedaling continuously. I decided he was nuts.
But then I bought a basket case Motobecane Mirage, converted it with Sheldon Brown's instructions, and I've been riding fixed ever since. My friend still has that old Moto, 8 years later, and I've done a bunch of other conversions since. Now I ride a proper track bike, a gang-green Pista, and a single-speed conversion.