The answer is horizontal dropouts. The only real difference with a SS specific frame is the long dropouts that allow you to move the wheel back and forth to keep proper tension on the chain. If your bike has vertical dropouts, like most modern bikes do, than you will most likely need to use a chain tensionor to keep the chain from falling off.

I haven't used these tensionors so I can't really comment on their performance, but I imagine that they add some resistance like a rear derailler and they may develop their own problems. One of the appeals of singlespeed is the clean look and simplicity of the bike so that could explain why people seem to eventually move up to the SS specific frame. Or some people that have a steel framed bike have the vertical dropouts replaced with horizontal dropouts.

Of course some people just like to buy new bikes, so maybe getting a SS bike is just an excuse to buy another bike.