I felt terrible that they had not be treated sooner. It only takes one infected flea to start the cycle. When they go to the bathroom, don't be afraid to look because if they have tapeworms the sooner you treat the healthier your pet. There are several other types of worms mentioned in the articles that I have listed below. Thankfully, I have not had to deal with these and can offer no first hand information.
Some common worms are roundworms and whip worms.
Well written article. Address the health issues and explains each type of worm. This article talks specificly about cats and internal parasites, including worms and protozoan problems. Uninvited Guests Discusses roundworms in kittens and explains that even healthy kittens could become infected. The article goes into details on the tapeworm lifecylce.