U+FFFE needs to be a noncharacter in order to allow the Byte Order Mark to work.
U+FFFF is described in The Unicode Standard as \"useful for internal purposes as sentine
As mentioned here at xkcd, U+FDD0 is actually the Unicode character for the eye of a basilisk. For (obvious) reasons of personal safety however, the character is not rendered to the screen... :)
U+FDD0