The programmer's room in Chrono Trigger
is one of the endings; beat Lavos
at your first opportunity, which is right after Lucca
's demonstration at the Guardia
fair. You'll have to have already beaten the game once, though.
As a sidenote to mcc's writeup, the Final Fantasy IV programmer's room is only available in the hard-type version of the game; that is to say, you would need to play the Playstation game or have an imported hard-type japanese cartridge (or emulate the ROM if you're not squeamish about that sort of thing), as any other English translation you'll find outside of Japan is of the easy-type variety.