In addition, optical hardware is becoming less expensive. On a per-port basis, the prices of routers and switches are approaching parity with that of copper gear. The most obvious choice for gigabit deployment is a network backbone, if it hasn't been done already. Gigabit technologies are highly appropriate for the server room, and if you're concerned that existing patch panels and other wiring system components aren't up to snuff, connections in the server room are the first ones you should replace anyway. Some user desktops may also be natural choices.
Any user pushing large masses of data to the network is a candidate for a gigabit connection.
If your cable runs aren't too long, you're not expecting to use the cable plant for more than a couple of years, and your installation is done competently, you can probably expect to get several more years out of a copper network. Otherwise, it's time to start thinking about fiber. Fiber networks can't be tapped this way because photons don't generate radio frequency emissions. Of course, none of this means that copper is going away anytime soon. So much is already installed, and people are comfortable with a familiar technology.