A great website came to my attention cinemagraphs.com. The work of Kevin Burg and Jamie Beck, the site shows their moving still images. These are animated GIF files that have one element moving within what is basically a still image. If you think of the moving photographs in Harry Potter newspapers you will have the right idea.
While they say little about the process on the site, it is a fairly straightforward process to recreate. The way I would tackle it is to shoot either a series of stills at high speed or HD video, and then pull single frames into layers in Photoshop. You would then erase all the elements you want stationary from all layers except one, leaving a stack of layers of the moving element(s). This could then be turned into an animated GIF using the Animation/Timeline window and turning layer visibility on and off as needed per frame.
The best work is extremely effective, whilst some is not quite as interesting. Definitely worth a look.