Technically you shouldn't expect serial comms to work unless the connection is 3 wires: tx, rx, and signal gnd.
If the two devices are sharing a power supply, then presumably (i.e. except when something more complex is designed in) they have a common ground and you may be able to get away with just two wires: tx and rx. For this to be guaranteed reliable the two devices should be on the same PC board or on boards connected via headers, so the integrity of the ground plane is assured.
If the two devices are not sharing a power supply, then you would probably want to opto-isolate the tx and rx (and gnd) on the board you care most about (if not both) so that differing (floating) ground potential doesn't cause big problems. You may be able to get away with enforcing a common ground, but then strange things happen with ground loops etc if there are other emf things going on nearby.