Why are there so many grounds for the parallel port? Are they paired up with the signal pins or are they all just a common ground and we just have a bunch of them?
Yes, they're all just grounds.
Basically, to support high data signaling rates, the ground connection needs to be fairly low impedance, otherwise you get all sorts of problems like ground bounce, which would lead to signal integrity problems.
For instance, a common PATA cable has seven separate ground connections.
Other interface protocols, like SCSI use differential signaling, therefore completely avoiding the problem.
There were several upgrades to the parallel port specification through the years, but yes each ground is separate, and later on they could be used for data circuits also.