Apple snails are not a parasitic snail (I do not know of any snails that are parasites). They may be pests to some, but others love them, as that classification is purely subjective.
Those with the nickname "Apple Snail" could actually be one of several different species of snail. Some have a reputation of eating plants in an aquarium, not just the algae. For Apple Snails to breed, you need a male and a female. If you keep only a male or males, you will not have more in the future. Females, on the other hand, are a bit tricky. While they do need to have contact with a male to reproduce, like livebearer fish, they can store sperm and produce fertilized eggs months after being seperated from the male. If you want to keep them as pets, and don't want them to reproduce, keep only one gender, and if you have females, watch carefully for eggs. Remove them if you do not want more.
This link shows many of the 'common' snails you will see in an aquarium:
Various freshwater snails
Many of the snail species are classifed as invasive pests, and it is illegal to have some of them in different parts of the world due to the possiblity of breeding and outcompeting the local fauna.