Android only: Live wallpapers can be pretty and ooh-shiny, but with WebLiveWallpaper, they can actually be informative and revealing. Keep tabs on a certain site, rotate great shots from Flickr, NASA or National Geographic, or even periodically check a webcam.
Developer Michael Haar initially started his app so he could keep an eye on what the waves looked like at his favourite surfing beach, but opened it up to allow any web page, changing image, or webcam feed to be used as a Live Wallpaper on Android. You can plug in the site or image yourself, "Share" it from your browser, or choose from the nice set of pre-loaded options in the wallpaper's options. Best of all, you control how much juice your changing wallpaper uses up by manually tweaking the refresh rate.
WebLiveWallpaper is a free download for Android phones only. It's in beta, but it seems to work well enough to do what the label says it does.