You could say that the biggest hard drive in existence doesn't exist yet. But the theory and capability to make the largest hard drive does exist. Unless you're talking about size, not capacity. We left the biggest hard drive behind decades ago.
Bigger is not Capacity
Since the computer was invented, it went from filling a room to fitting in your pocket. In 1956 a hard drive weighed just over a ton and held only 5 megabytes. In 1989, one of IBM's hard drives weighed 85 pounds, but only could contain 1 to 2 gigabytes. It was large in size, but tiny in capacity. They had to use several of these puppies to run a Direct Access Storage Device. Of course, by then there were smaller hard-drives, but this particular hard drive was all about reliability; the bigger, the more reliable (so was the logic).
So what is the "biggest" hard drive for capacity? Currently the largest hard drive you can buy is 4TB (which makes IBM's 2 gigabyte hard drives look minuscule). But it may be within a decade that our children will say, "4 terabytes? That's so small!"
In 2012, Seagate announced its breakthrough in hard drive technology. Instead of using perpendicular magnetic recording (PMR), Seagate uses heat-assisted magnetic recording (HAMR). With this technology, Seagate can now fit one whole terabyte on a square inch (2 billion bits). It was once thought to be impossible, but now it's estimated that by the end of the decade, hard drive capacity will reach 60 terabytes.
Meanwhile, other innovations are hyping up the capacity levels. Western Digital is producing a 5.6 terabyte hard drive by using helium. The helium will solve several problems. Helium has 1/7th of air's density, so it produces less drag than air. With helium, the disks will spin more smoothly, therefore enabling researchers to fit more bits onto the disk. Plus the lower turbulence allows Western Digital to place two additional disks into their drive. (Typical hard drives hold only 5 disks). We'll see what Western Digital is able to achieve with this new innovation.
The biggest hard drive in existence is constantly changing. Each year there is something new to take memory capacity further. We went from having to heave our hard drives on cranes, to simply slipping them into our pockets before going to work. Our hard drive capacity went from megabytes to terabytes. But we want more. We want the largest capacity placed in the smallest and most elusive containers.