Cinemagraphs might be the best things ever. Not to be confused with normal GIFs, cinemagraphs are seamless animations of stills that usually contain mostly stationary elements. The elements of the animation that do move are subtle and loop so cleanly that you can't always spot the beginning or end of the clip. There are apps for this, but they don't exactly measure up. The term cinemagraph was coined by Jamie Beck and Kevin Burg, graphic designers who first made the animations out of their fashion photography.
This Tumblr combines cinemagraphs and cinema, taking stills from movies and turning them into mesmerizing animations.