The "Ping of Death" was a nuisance that first reared its head in the 90s. It allowed someone to effectively denial of service someone's computer with a single packet.
A patch was quickly released for linux distributions but the patching process for Windows machines wasn't so speedy. The majority of people online were using slow dial up connections and simply did not have the time, or the inclination to download and install security patches.
At present most people have a router between their home network and the network. To an extent your computer is pretty well protected by your Netgear NAT enabled router. Back when the Ping of Death was prevalent you had no router and Windows didn't have a built in firewall. It was up to the user to install a firewall and antivirus.
With an army of unprotected and unsuspecting users directly connected to the Internet it didn't take long for the Ping of Death to become notorious. Online gamers could crash their opponents computers if they felt the need for revenge, IRC users would knock their enemies offline with ease.
Now a days you need an entire army of drones to knock people offline but back then all it needed was a small tool easily downloaded from the internet and your targets IP address. Some of the tools allowed you to work through entire IT ranges.
The news that IPv6 stacks on Windows platforms may once again be open to such attacks isn't as alarming as it could be. As a victim you're going to have to have your PC connected directly to the internet and you will need to be using an IPv6 enabled Internet connection (which you're probably not).
A more likely scenario will be if the attacker is on your network. Ping of Death was a favorite in the script kiddies toolkit and with IPv6 enabled by default on Windows operating systems I imagine some mischief is to be had in some high schools with the attacker and victim probably sat in the same room.
Serious security breaches will need some assistance of trojan horses or other methods to generate network traffic from inside your network. If you're in that situation then I think the ping of death is the least of your worries!