Kittens are like children, they may get sick and nobody can guarantee absolutely that you will never have a problem. The most common ailments are upper respiratory infections that have symptoms much like the common cold (runny eyes, nasal discharge and sneezing). All my kittens are vaccinated against the more prevalent kitten viruses but sometimes the stress of being moved into strange surroundings can trigger a problem that has been lying dormant.
All kittens have been checked by a local vet prior to sale, you have one week to have your own second oppinion from a vet of your choice. However, all kittens will come with written documentation that they are free of parasites, genetic problems or other ailments.