well in my family of sunes there are -
sune, fatty sune, double sune, double fatty sune
anti sune, fatty anti sune, double fatty anti sune (i love that one)
lefty sune, fatty lefty sune, fatty lefty antisune
and then all of those from the back...
...and finally supersune for the megaminx.
many of these are kind of arbitrary - just to avoid having to do an extra U/U2 turn.