Here's a great compilation of short films that were eventually made into full-length films or television series, including Marcel the Shell with Shoes On, Brian and Charles, Shiva Baby, Thunder Road, Pixels, Whiplash, What We Do in the Shadows, The Babadook, This is the End, Frankenweenie, District 9, Inland Empire, Napoleon Dynamite, Saw, Boogie Nights, Hard Eight, Bottle Rocket, True Romance, Reservoir Dogs, and Fatal Attraction.
Robert Lang of Deadline explains:
Writing and directing a short is a potential passageway to creating a full-length feature film. Aspiring directors use this medium to create a proof of concept on a small budget that can go on to win on the short film festival circuit and be picked up by investors, leading to larger projects and paving the way to a career in Hollywood.
I think my top pick of the bunch is the short film "Peluca," which led to one of my all-time favorite films, Napoleon Dynamite:
The 2003 short film Peluca on which Napoleon Dynamite was based, shows a day in the life of super nerd Seth, starring Jon Heder, skipping school with his two friends, picking up a winning lottery ticket, and thrift shopping. Director Jared Hess made the proof of concept for the film which would go on to be a cult classic.