Any move where the board doesn't leave the water:

Backside Butterslide
Rider turns the board backside 90 degrees and grinds the water

Backside Butterslide 180
Rider turns the board backside 90 degrees and grinds the water
Rider then grabs the bar with opposite hand and does another 90 degree turn in the same direction.

Body Slide
Rider lies back onto the water.

Butterslide
Rider turns the board frontside 90 degrees and grinds the water

Butterslide 180
Same as regular butterslide but with an additional 90 degree rotation in the same direction

Perez
Rider slides into a surface 360

Potato Peeler
Body Slide with fin release

Powerslide
Board is turned backside 90 degrees. Fins are broken loose.

Surf Carve
Rider cuts back and forth in a surf-carving fashion.

Surface 180
A 180 degree turn on the surface of the water.

Surface 360
A 360 degree turn on the surface of the water.

Tumble Turn
Rider lays back on water, board is taken out of water and above the head, body is spun around backside and the rider stands back up onto feet.

What the fu......?

I take it that you haven't seen or done one of these???

PMU

Sounds like something a barefoot waterskiier would do...

HAHAHAHAHA I HAD THE SAME RESPONSE.

A lot of riders do this move, especially mutant riders. Check out footage of Flash Austin or Mark Shinn, they do this regularly. The typical sequence of events goes:
1 Approach transition point riding toeside with forward arm's hand scraping the water.
2: At the same time as you move the kite to the other side of the window, do a forward summasault over your forward hand
3: Stand up while driving your kite into the window in the opposite direction from which you entered the tumble turn

PMUs right. i've seen guys do this move, it looks quite cool. Sometimes it happens when guys try their first spins and they end up doin one of these... they look way cooler than proper spins too!