all the folks saying 65,535 are correct.
HOWEVER!!!with some careful kernel tunable parameter manipulation you can tell linux to use more. Some commercial UNIX systems would run services on technically out-of-bounds ports with no problems. Super simple way around some of the firewall/ACL protected networks too! :P
I used to run a second telnet server on tcp/99999 and it always worked for me. Even in cases where the typical privileged ports (1-1024) are blocked by ACL or network firewall.
Almost nobody scans for ports listening above 65,535. Most network equipment cannot inspect anything outside the defined range (0-65535) and blindly forward the traffic unless instructed to do otherwise by rule.Now that we have 64-bit systems, the upper range is technically the 64-bit boundaries. Doesn't mean networks will pass the traffic, but typically they do pass anything there isn't a rule to drop or deny.