I am replacing an old circuit panel with a newer circuit panel with a 100 amp main breaker in it. Do I have to run a ground pole in to the earth and run bare copper wire to the circuit panel?

Possibly will need to be done. The original system must have been grounded somehow, and it does not necessarily need to be done at the panel containing the Main Breaker, could be grounded at the meter.

Happen to see a ground wire leaving the meter connecting to a metal water pipe and/or a ground rod?

Well, there are three wires coming from the meter to the service pane. Two are connected to the 100 amp main breaker and one is connected to the neutral bus bar. There a ground wire that runs from a water pipe to the neutral bus bar inside the service panel. Is this right and should I still do a grounding rod?

If you noticed I did mention a possible ground connecting to a water line.

This is your primary grounding electrode. Your existing service could be old enough that at the time of install, that was all that was required.

New code requires when a water line exists, it to be used as a electrode, but that at least one ground rod be installed to supplement the water line.

Best to check with local codes to determine if more than one rod is required.