Mew, Celebi, Jirachi, Arceus, Victini, Reshiram, Zekrom, Keldeo, Meloetta, Xerneas, Yveltal and Zygarde are Shiny-locked.
All of them (aside from the XY trio to the best of our knowledge) DO have shiny palettes, but there is no way to obtain them legally - their shiny palettes were programmed into the game to prevent the thing from crashing in case someone fucked around with memory values/gameshark codes - for the very same reason that Arceus had a ???-type form in Generation IV (this was removed when the ???-type was removed as a whole in Gen V).