I use special characters in 3 of my 4 armies i own. Why not.
Astral claws: lugft huron is such a fundamental figure for them that it seems less approppriate not to use him.
Sisters: celestine is probably your only hope of competing at all in melee.
Grey knights: i built an adeptus custodes list so draigo lets me use paladins as troops and these guys are the only guys fit to represent the emperor and his custodes.
Tyranids: i dont use any of them, the dooms too eratic and the pornlords save isnt as good as id like.
Broken units? The vendetta. Cheap as chips and reliable. Units must be able to reliably influence games to a winning conclusion to be really classed as broken.