Manx cats are world famous for being Tailess, having one myself I have been very interested in how they became like this and does it effect them. There are count pages on wikipedia with all sorts of advance details about the nature of the cat, but here I will be putting it a whole lot more simple. Manx cats do no behave any different than normal cats. The taillessness arises from a spontaneous mutation, the Manx taillessness gene, that became common on the island because of the limited genetic diversity of island biogeography (an example of the founder effect and, at the sub-specific level, of the species-area curve)
A lot of people think that all cats have a disease called spina bifida but they dont, here is an extract from wikipedia - "Manx syndrome" or "Manxness" is a colloquial name given to the condition which results when the tailless gene shortens the spine too much. It can seriously damage the spinal cord and the nerves causing spina bifida as well as problems with the bowels, bladder, and digestion. Some live for only 3 years; the oldest recorded was 5 years when affected with the disease.