Why are there so many connections to ground in some computer connectors?

For a power connector: each pin can carry a limited amount of current. All current must return via ground. There are multiple power pins per voltage, hence multiple ground pins are needed to carry all the ground current.

For a data connector: unused pins might as well be connected to ground, and when a ribbon cable is connected, subsequent wires are alternately connected to the top and ground row, hence the ground pins end up connected to wires that sit between signal wires, which add some extra shielding between the signals.

For the ATX power supply cable there needs to be enough GND wires to return current from all the other voltage rails back to the power supply. So ideally the number of GND wires would match the size and number of the voltage rail wires.

For the parallel port you need multiple GNDs so that the return current path for the signal lines is reasonably balanced against the number of signal lines. Ideally the number of GND wires would match the number of signal wires and each would work as a twisted pair in the cable.