When using Spaces, is there a way to set each "desktop" background independently?

For instance, say I had a few sweet background images I wanted to use to identify each one.

There's no built-in feature in OS X for that but there are two applications that can do that for you, Hyperspaces and SpaceSuit.

Mac OS X Lion supports this out of the box now. Simply switch to the Space you want to apply a certain background to, then change it as usual (with System Preferences or the desktop's context menu). Repeat for your other Spaces and background images.

For older versions, you will still need to use a third-party tool as recommended by the other answers.

You have to use a third-party tools, like SpaceSuit.