In addition to Carl's comment I want to add that a rigid copy protection system can make users really annoyed and so a good software becomes a bad software.
Other than that it really depends on the software what to do - can you expect internet connectivity or might the application be running in a data center behind many firewalls? If the net is available an auto-update service is a nice way to track usage - while you should take privacy into consideration then. Otherwise some random serial number process is often good enough: Those who take the effort to bypass it most likely won't buy the software anyways and for others copy and pasting a serial number might be acceptable. But then again: It depends on the software and the users and ...
Punishing the paying users and making it harder to use the software legally than illegally certainly won't work out.
