Lungworm larvae may be present in slugs and snails, and if eaten, pets may be infected with worms that make their way to the lungs, where they block airways and make breathing difficult. Most dog wormers don't claim to treat lungworm, although some cat wormers do. Research conducted internationally has found moxidectin, which is found in some heartworm treatments for dogs, to be effective against lungworm, but this claim can't be made for dogs on packaging in Australia. Check with your vet as to whether it's an issue in your area, and discuss the best preventative treatment.
Puppy Roundworms can infect humans. To prevent this infection, puppies should be wormed regularly throughout their first year of life, and owners should be thorough with their own personal hygiene after having interacted with the dog. Tapeworms, Hookworms, and Whipworms can also infect dogs, and your veterinary surgeon can advise when to worm the dog.