I'm pretty sure they are species-specific. You can get ringworm but that is a fungus on your skin, not an intestinal parasite. Generally to get any intestinal parasite you have to ingest the eggs (eat poop or bite your fingernails that have poop/eggs underneath etc.)
Always a good idea to wash hands after dealing with any animals.
Around-I was told by my veterinarian that the only species that is afflicted with pin worms are humans, and you don't want to know how we get them (plus they eventually die off by themselves supposedly). And you can get hookworms from them burrowing into your skin (at least that's how I remember it, and I could be wrong).