Do dogs carry skin diseases, like ringworm, that can be transmitted to humans through touching?

Diseases from dogs. Diseases that can be transmitted from dogs to humans are rabies, ring worm, leptospira, brucellosis, campylobacteriosis, tapeworm, giardiasis, hookworm, leishmaniasis, q fever, rocky mountain spotted fever, roundworm, salmonellosis, lyme disease, cryptosporidiosis, toxocara infection, flea tapeworm.
Yes. Pets are a common source of infection with skin fungal infections (ringworm).