I have moved 4 romex cables (4 different circuits) from the old main panel and ran them into a 8 x 8 pull box. I then ran new romex to the new main panel 20 feet away and made the connections to the panel and breaker. Is it OK to connect all the ground wires from the 4 circuits together in the 8 x 8 pull box or should they be kept separate?

All ground wires can be connected tohgether, or separate, does not matter which you chose.

Ground wires yes, neutrals no.

Good point.