If I were to be immortal, my thought is that it would happen this way: I would age, then fall into a coma, as my body rebuilt itself. It would take a few weeks, in which doctors would be scrambling to find out what is wrong with me. Then they would realize my telomeres are rebuilding, and that my body demands more sustenance. This would come to the attention of the muckitymuks that study strangeness and hold it for government need to know. So when I awoke, basically I'd be in debt to the government. No problem. They would study me; in turn, I would be physically retrained (after all, the body may remember, but muscles still atrophy without use). Then I would try to bargain; I'll work and stay the government's secret in exchange for a tour of duty as a Marine (including boot camp) and schooling in various languages and countries - I would spy for them, me with my dark little self looking more like a servant than a diplomat.
I daydream about this; the chance to relive my life, my way. It's great fodder for all sorts of fantasies I could not even think of living now. And it's a nice escape.