Exposure, Sci-Fi Channel
IMDb; Sci-Fi (archived); TV.com; Wikipedia
This began in April 2000, and ended, I think, in March 2002. Each week they showed several short films in an hour. I didn't like all of them, but a lot of them were pretty great. The first season didn't really have a host, maybe an occasional guest host. The second season was hosted by Lisa Marie. I wish I could think what else to tell you.
Partial list of films aired on Exposure
The things I remember best from the show include "9mm of Love," "Accident," "Evil Hill," Frankenweenie, Fulfilled: A Halloween Story, George Lucas in Love, Graveyard Jamboree, The Hole, "Hollow," More, "Redshirt Blues," "Suspicious," "Tripping the Rift" (which led to a series of the same name), and Vincent. Maybe a few others, to a lesser extent. Someday I'd really like to watch all of those films again and review them, and probably some of the other ones I don't remember well at all.