I know that digital sensors have filters that filter out UV and IR light and thus do not require UV filters, but what about film? Are IR or UV filters required when shooting film?
"Required" is probably a bit of an overstatement, but they are certainly more useful for film shooting.
The exact effects that UV have on your film photographs will depend largely on what film you're using, and the conditions under which you shoot. From the Wikipedia article UV filter:
Historically, some photographic films were sensitive to UV light, which caused haziness or fogginess, particularly with a blue hue. However, newer photographic film and digital cameras are highly insensitive to UV wavelengths.
I bought a used Minolta with UV filters on both lenses. One day while shooting, I took it off half way into a roll of 200 speed film. The shots were super sketchy after that, so if you are shooting outside in bright sun with film, I would recommend it. But, that's just what I think — could be different with different film and different cameras.