Yes, I sometimes download and try out demos of PC games before I buy them if I'm not sure if the PC game is worth it, or to see how good it is before I buy.
Since I own a slower and older computer, I am more likely to try out the game to see how it runs on my PC before I buy.
But, If it is a game that I know I'll love like Warcraft 3 then I just buy it without trying the demo.
It depends upon my mood. At times, I download free demos to get a feel of the game, its graphics and gameplay but when I already know that a game is good in these departments, I do not bother with free demos and straightaway buy the game.
Yup, just to add on to my last post here, I recently found a game that looked interesting, Naval War: Artic Circle, but wasn't sure so I downloaded the demo. I'm glad I tried it out before spending my money, it wasn't really my type.