A unique short film, La Jetée is composed of still photographs which tell a story of time-travel and a post-apocalyptic world. This was the short that inspired the movie 12 Monkeys, so if you've seen it I suggest you watch this.
The only film that I know of with a similar format is Greed (von Stroheim, 1924), but in this case the still photographs were used to make up for lost footage.
I've found it on youtube, split into three parts of about 10 minutes each. Enjoy.