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 (who we like). 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, 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.