If you find a tick, send it to a testing center to determine if it's a carrier. You may want to spray the area for fleas and other pests. Ringworm is actually a fungus and can be transferred to both humans and other animals. It makes cat fur fall out in a circular area, and the skin underneath will look red. Wearing gloves will protect you.
Many internal parasites live in cat feces.
Toxoplasma dondii is a particularly nasty one that can be passed on to humans. In pregnant women it can lead to abortion or fetal abnormalities. If you're pregnant. Everyone should wear gloves and wash their hands well after cleaning litter boxes. Cleanliness and a little precaution will reduce or eliminate most health risks.