Most modern games use TCP/IP networking rather than a direct serial or parallel connection. This means you'll need a TCP/IP stack (Miami, Genesis etc.) on each machine and a PPP or SLIP connection over the serial port. There is also a SANA 2 driver (PLIP) for TCP/IP networking over a parallel cable but I've never tried it.
After you've got that setup then any game that uses TCP/IP should work well. You might find that performance is limited by the speed of the serial port and the fact that at higher transfer rates it uses a lot of CPU time. A fast serial port add-on could help there but if you're going to spend money it's worth considering an Ethernet setup.
Robert