"Cryonics" is the correct term for preservation of legally dead humans in anticipation that future science can cure their diseases, rejuvenate them to the prime of life and fix any damage caused in the process of cryopreservation. "Cryogenics" is low temperature physics. Those who use the word "cryogenics" to refer to "cryonics" are people who have not seriously investigated the subject.
Cryonics has been not been proven to work because it is dependent upon future technology to work. The real question for someone seriously evaluating the value of cryonics is whether the necessary future technology is likely to exist. That technology must involve molecular-level repair of damaged molecules or wholesale replacement of tissues with new tissues. Nanotechnology (or nanomedicine) and biochemistry are moving in the direction of increased capacity for molecular level repair, and stem cells seem promising for tissue regeneration.
Legal death is typically pronounced when the heart stops. But stoppage of the heart is not the same as all of the tissues in the body being dead. The process of decomposition takes days. If the body can be quickly cooled after pronouncement of death, and blood replaced with an antifreeze solution before cooling to liquid nitrogen temperature, then the basis of consciousness (the brain) can be retained for future molecular repair and rejuvenation.
Cryonics is not a "final solution" against death, any more than penicillin, kidney transplant or seat belts. Cryonics can make a very great difference in lifespan (if it works), much moreso than almost any medical procedure. But cryonics cannot prevent death from nuclear war, drowning while lost at sea, dying in an airplane accident or being trapped in the World Trade Center on 9/11. Things that destroy your body will kill you in a way that cryonics cannot hope to deal with. Once you have been buried for a few weeks or cremated, cryonics is not going to be of any use.
Science offers much evidence that cryonics is plausible, but future technology can never be proven. Cryonics can be an attractive alternative to burial or cremation, but if being alive is the goal, cryonics is the last resort (although it definitely helps to make plans ahead of time). As many of the previous answers show, being alive does not have great appeal to many people, including atheists, who apparently only remain alive in passive continuation of their current condition. Such people will not be candidates for cryonics, but they will generally accept existing life-saving medicines. On the other hand, there are theists who are eager to make the most out of life on earth who eagerly seek all available options to extend their lives, and in some cases this includes cryonics.