The GIF, first created in the static format by CompuServe in 1987, emerged into animated prevalence in the ninetys with the introduction of Netscape Navigator 2.0 (remember the logo with the shooting stars).
Recently, animated GIFs have been making a comeback in the form of cinemagraphs (still images with a minor animated element to create a dramatic effect). One cinemagraph artist, Gustaf Mantel, uses animated GIFs to capture epic film moments from directors such as Stanley Kubrick, David Lynch, The Coen Brothes, Fritz Lang, Danny Boyle, Wes Anderson, Quentin Tarantino, and Roman Polanski (to name a few). I was first introduced to this concept by Fast Co Design. Take a look at a few of my cult favorites.
Blue Velvet
Fargo
Fear and Loathing in Las Vegas
Lost Highway
Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb
The Big Lebowski
The Royal Tenenbaums
The Party
No Country for Old Men
Eraserhead
Pulp Fiction
Twin Peaks: Fire Walk with Me
Trainspotting
Metropolis
Ghostworld
Rushmore
Fahrenheit 451
Blade Runner
The Life Aquatic with Steve Zissou
Rosemary's Baby
A Clockwork Orange