The most basic of animation effects would be to replace a specific texture with a movie/animation file (that is just a series of images.)
Then there is already a "water" animation: applying the shading element of this to grass or leave textures should be able to reproduce ripples and animation in other surface assets. It could also be applied to smoke or flame assets to give them some life.
Edit: Actually I would love to see an animated bump-map that could be applied to textures - you could produce wake ripples, raindrops, moving scales, waterfalls, ...
The next step would be actually manipulating the points that create the geometry of existing assets in 3D space. This could be used to open doors or move ducks on a pond.
Then there is an in-between stage where you sub-divide a surface to create points on it, then agitate these points. This could be used to create true 3D waves that would be seen at the union of 'water' planes and other surfaces or curtains that blow in the wind.
Then you get "true" animation where one set of 3D geometry is transformed into another set of geometry over a specific time-frame.