Linking movement of objects in 3D space and UV space.

Is it possible to link the movement of objects, faces, vertices, etc. in 3D space as well as UV space? Once I unwrap my object I’d like to be able to slide parts of it around and have it move correspondingly in the UV space. Thank you.

Moving faces/vertices:
Hook them to an empty, animate the empty / or make shape keys

Moving textures:
You can make the texture translation/orientation dependent on another object or empty.
Check out plasmasolution’s sneakpeeks nr.21 (at around 13 min):

Of course for animating texture coordinates you can also animate the Offset settings in the Texture panel / Mapping section…