In VMware Server, you can only ever have a SINGLE snapshot of a VM. You click the "take snapshot" button and it will overwrite the old one.
However, it turns out that you can easily copy VMs. Simply copy the folder to a different location. Open the VMware Server Console, open a new virtual machine by clicking the "Open a virtual machine" button, select the copied folder by browsing the computer - it will not show in the list, check the new VM's settings by clicking the "Edit virtual machine settings", then start it by clicking "Power on this virtual machine". Create a new unique identifier when prompted. That's all there is to it!
One final point... Because a VM consists of just normal files within a folder, you can back it up by copying (and zipping) the folder.