Here's some stuff that would cause a problem is they happened, but that I don't think will happen:
Mind body transfer
People living forever
Artificial wombs
Here's some that might happen:
Prenatal genetic selection, or alteration
Human cloning
Very expensive treatments that can not be afforded by many
Having children very late in life (i.e. within
a decade or two of expected death)
I don't know if it's possible to get it, but try to watch the show Century City, or at least read episode synopses. Your question is the premise of the show.
People living for a very long time could happen, but I doubt that the technology would be released to anyone who could not afford a few millions. No matter how cheap, whoever owns the tech can charge what they want for it, and people will pay tens of millions for it. It's better to concentrate on the high end market, than to go for the low end.
