typing in what kind of music you like and discovering music was the entire premise of Pandora and it was pretty successful.

You can easily comes up with "song/band sounds like X" but it'd be a lot harder to do with movies and TV shows because beyond genre there's a lot of variation in what makes something good. Acting, direction, lighting, story, effects, actors, etc. Failing on any one of those things means I'm less likely to enjoy a show, but being similar in any one of them could cause a match.

That said, if you were to ask for specifics it might be more helpful. Recommending movies based on tone, or style, or story elements might still be interesting but I think you'd still run into the problem where it may not easily result in something you're likely to enjoy.