Check your local newspapers and local news websites about "dumping events" where you can get rid of stuff like old desktops. The Whole Foods Market in Cincinnati has had two such events in the last 9 months alone.
The best thing to do is either donate it to a charity or have it recycled. A lot of places like Salvation Army and Goodwill will take them and sell them on for charity. Otherwise take it to a recycling place that takes electronics or contact your local computer repair shops to see if the want it.
If the desktop works, you can donate it to any number of community programs that use donated PC's for kids, you can drop it off at a local thrift shop, and many recycling places take old PC's.
I haven't done this yet but I have one that is soon to be disposed. I am planning to remove its hard drive just to be on the safe side. I know that a lot of important personal information are stored on that drive and then I'll donate the rest of its parts. Hope that helps.
