There are people who completely blind or deaf. Are there people who are completely blind to touch in a particular area or in the entirety of their body? If not, are there people in whom the temperature modality of touch or the pressure modality of touch is completely absent? It seems that this might be related to congenital insensitivity to pain, but it is not quite the same thing.
In a way, yes.
One prime example where the sense of touch is diminished is when peripheral sensory neurons degenerate, which is called sensory neuropathy. Diabetes is currently a common cause of this disorder, resulting from the high blood glucose levels that damages the small blood vessels which supply the nerves. This prevents nutrients reaching the nerves, eventually damaging nerve fibres, which may end up in a disappearance of the nerve altogether (source: diabetes.org).
Sensory neuroptahy can lead to a multitude of complaints, including weakness, numbness and pain, usually in the hands and feet (source: Mayo clinic).It can also lead to the loss of ability to feel pain, changes in temperature and coordination when you lose proprioception is affected. The loss of the sense of pain is dangerous. An often heard complaint is that wounds to the feet are not noticed. If ignored, even minor injuries can develop into infections or ulcers (source: diabetes.org). I fact, my grandmother-in-law recently underwent an amputation of the lower leg, because of a diabetes-related, neglected injury to her toe. It lead to an ulcerating wound and eventually necrosis. At a certain point it caused terrible pain, but the initial wound had gone unnoticed.
A related condition is Carpal Tunnel Syndrome, also called median nerve compression. It is a condition that causes numbness, tingling, or weakness in your hand. It is caused by pressure on the median nerve that traverses a passage in the wrist called the carpal tunnel.
This may not be exactly the answer you are after, as sensory neuropathy mainy causes numbness of the extremities, rather than a complete loss of sense of touch. Remember, however, that blindness rarely results in a complete blackness. Beside the fact that the great majority of blind people are 'only' functionally blind, as they still have rudimentary visual function left, perceptions of phosphenes are in fact really common, and some people even start seeing complete visual scenes with people and objects included (Charles Bonnet syndrome). This is not unlike deafness, where many people still have residual hearing, yet too little to be of any functional use. For instance, people that are eligible for a cochlear implant often still have substantial residual hearing left. Like phosphenes in the blind, tinnitus in the 'deaf' emerges akin to 'phantom' sounds. These 'hallucinatory' sounds are actually generated more centrally by the brain after prolonged deafness. In short, blindness and deafness are relative, the great majority of folks don't lose their senses, they have reduced functionality of them.