Major websites now supposedly support IPv6 including Google, Facebook, Verizon, and Netflix. Check out Facebook's IPv6 address in this screen capture from using nslookup:
Someone has a sense of humor! (Ya gotta love engineer humor.)
World IPv6 Day is June 8th, when major providers will be enabling IPv6 on their networks (many have already enabled it).
You can test your IPv6 readiness at http://test-ipv6.com/, which is good for hours of entertainment. That same website has an entire page devoted to IPv6 day.
Yes, conversion to a new transport protocol is challenging and potentially dangerous. Yes, it will happen eventually, so you might as well start the process of preparing now. See my previous posts for more information about the changeover process, including websites for more info about how to do it.