If you're running a small in house server for you company for their computers, you won't probably need it.
For the rest of the web, IPv6 is something happening right now and you NEED to support IPv6, because there are many and many people joining to the IPv6 network and the transition between the two represent lose of service and delays, so yes you server really need to get an IPv4 and a IPv6 address. IPv6 is also great in other conditions like in media stream because you can just send one packet to multiple clients at the same time instead of sending the same content repeatedly for multiple clients — Less bandwidth needed to live stream.
For instance in my country, Portugal, out brand new optic fiber network is covering 90% of the country and it's fully IPv6... So I guess that other countries are doing the same now. There are no IPv4 addresses—we ran out of them ;)