Whether or not burn-in occurs depends upon the
display technology used.
There are a total of five completely different technologies used today to create an image: Cathode-Ray Tube (CRT), Plasma, Liquid Crystal (LCD), Digital Light Processing (DLP), and Liquid Crystal on Silicon (LCoS). Only the first two are susceptible to burn-in, and Plasma is not a projection technology. Plasma and CRT, as they rely on the stimulation of phosphors, suffer from burn-in when an area of phosphors is held in the same state for too long.
The other four technologies are used in rear projection, and the two reflective technologies (DLP and LCoS) are immune from burn-in.
In other words, a CRT-based rear-projection display will suffer from burn-in, but a DLP- or LCoS-based rear-projection set will never suffer from burn-in of any kind. As mentioned, Plasma is also susceptible to burn-in.
LCD has a related burn-out problem, but it is not pattern-related. Since the light in an LCD projector passes through the LCD itself, the heat and light slowly destroy the crystals and polarizers. This results in a washed-out display.