There is no "private" IP addresses in IPv6. (There is LinkLocal, but that is a bit different).
NAT Will no longer exist. Most companies trialing it, such as comcast, are giving out 32 bit addresses to each consumer modem. that would give you 4 billion IP addresses to use with your connection. (right about how many IPv4 Addresses there are in the world right now)
Firewalls will still be critical, but will not have to do NAT anymore. Things like person to person video chat will really work correctly.