All computers on aircraft in our fleet have been certified Y2K compliant (DC-10, 320, 321, 330, 757, 767). As far as Boeing and Airbus are concerned the computers will handle the date change with ease, and even if they don't no serious consequences will result (except that the date will be wrong!).
The concern has been with ATC systems particularly in countries like Greece, Spain and Turkey. The media-generated image of aircraft falling from the sly because the computer has failed is rubbish. Somehow today's image of planes being flown by computers has pre-empted this idea that planes will not be able to fly at all if the computer does not work! The laws of Physics will not change, even an A320 (oh yes Boeing lovers!) will fly perfectly well without computer assistance.
The main other reason planes are being grounded is the severe low demand for flight bookings over this period, or gicing staff a holiday (not the fear that an airline's shiny new 747-400 will end up a lump of metal!)