Nicely done still photos with partial looping animations are meant by the term “Cinemagraphs”. I just saw them popping up at various blogs and galleries. Browsing through tumblr using the tag “cinemagraph” reveals quite a nice selection. Gonna try this when my current projects are finished.
The funny thing: By accident I did a very simple cinemagraph with my last entry, where I’ve shot two photos. One with the cursor and one without and animated it.