But an organic brain in a cybernetic body? How long would an organic brain continue viable? Wouldn't the cells decay?
Eventually, technology would probably make it possible to create a fully digitized version of the functioning human brain. That would make it possible to upload ones sentience into a computer. Another alternative is that nanotechnology will progress to the point where a functioning brain can be fully reproduced with inorganic nanotech neurons capable of "reproducing themselves" indefinitely (once energy and raw materials are available) without deteriorating (aging).
I don't think technology will necessarily lead to guaranteed immortality, though. There will always be unforeseen accidents, murders, technical failures, etc. But the prospect of resurrecting persons would definitely be plausible and "human" lifespan - the lifespan of the human mind - will likely increase greatly - hundreds of years at least.
But before this happens - or perhaps in order for this to happen - computer scientists will likely have created the first true artificial intelligence - the first autonomous, self-conscious artificial being. Imagine the legal, social and ethical controversies that will result! We might see the return of institutionalized slavery of intelligent beings, only this time, the intelligent beings will be denied the dignity of being treated like humans simply because they technically aren't. But I think it would be the religious who would advocate not treating them fairly, arguing that they don't have a soul breathed into them by God. But secular, science-based society would argue that they essentially have the same cognitive attributes as humans, and there is no such thing as a soul and so they should be given the same dignity as humans. This could be the defining controversy of the future, dwarfing the current Evolution vs Intelligent design education; and pro-life vs pro-choice controversies, combined. (BTW, have you guys seen the new series Humans? It is just awesome!)
This may all seem rather fanciful but the progression of human technology makes it very plausible. Imagine how fanciful the notion of landing on the moon, would have seemed to people living 500 years ago. But today, humans landing on Mars doesn't seem far fetched.