I just received a new Galaxy S4. I was wondering could I just insert my SIM card from my S3 into the S4 and the phone would work. If not, could I duplicate the card and have the option of using either phone.
If they are the same size, just move the SIM card to the new phone. You can't have two active SIM cards associated with the same line.
As Ann said, you cannot have two sim cards for the same number active at the same time. You can however remove the sim card from one phone and put into the other whenever and as often as you wish. That makes the other phone a small sim-less, WiFi only tablet. :-)
I have been informed by one of the more reliable VZW reps on this site that you can swap the SIM card four times between phones four times max in one billing cycle. I have switched four times in a cycle, but I haven't tried for the fifth time to verify that the is in fact a limited number of swaps allowed.