The Movie: Khan and his crew were put into cryosleep for hundreds of years. But when he woke up, he started being a badass right away.
Real Life: Cryonics is a fascinating field, and it's always making progress. Bodies can be preserved at freezing temperatures, and indeed, hundreds of people have been frozen by cryogenic researchers. The problem is the waking up part. Bodies are frozen after death, in the hope that one day, there will be a technological breakthrough capable of reviving them. Many believe nanotechnology will offer such an advance, because it has the potential to repair damage on the molecular level. But a lot of scientists are still skeptical, especially neurologists who point out that the brain is not something you can just switch on and off after hundreds of years. Not even if you are some kind of genetically engineered superhuman like that cutie pie Cumberbatch.