The self is defined by your memories and experiences (and some genetics). Those are stored in your brain in synaptic connections. As long as your brain stays in tact, 'you' are still there. However the brain needs continuous maintenance, when the blood flow stops it will start decaying. All your memories that define you will be irrevocably lost. You will cease to exist.
Some people hope to cheat death by freezing their brain or entire bodies. Whether that's enough to restore brain function in the future is unknown. (But a hell of a better chance then cremation)
Reincarnation doesn't mean anything to me. Since you can't remember your past live(s), that self has been lost.
A lot harder question is what is consciousness and when does it start. I don't believe consciousness can survive death. I think it's part of your brain processes.
Another interesting ethical debate for the future. If computers ever get advanced enough to make it possible to scan and copy the vast neural network of your brain into a computer network and provide all the sensory connections, would you be comfortable experimenting on yourself. Are there 2 of you at that point.
What would you do with your 'old' self after uploading, you're still there. Now there is another you that starts diverging from you just after the upload.