Can my canon lens from my 35mm camera work on a digital body?

I have a Canon EOS Rebel X 35mm film camera. The lens is EF 35-80mm. I don't know much about camera's so not sure what other information i should include with my question. I want to upgrade to a digital Canon camera but was wondering if my lens from the old camera would work on a digital canon body? And if so, which camera would it work best with? It also is a manual/automatic lens if that necessary to know. Thanks for any help.