Alligator dog - this is when he is resting on his stomach, his full five feet length in a straight position. His long snout and large black nose gives this pose its name.
Crescent dog - here we see him curled slightly in the shape of Pillsbury's finest.
Circle dog - here he's tightly curled, tail to nose, in a circular position.
Carpetbagger Dog - not a pose but a tendency to relocate to where you were sleeping after you get up.
Flat dog* - here he lies on his side (colloquial usage: flatamaran).
Centerfold dog - he's flat on his back, package to the wind.
And some non-sleeping descriptions:
Necktie dog - sits alert his with his neck craned as if wearing a necktie.
Begasaurus Rex - self-explanatory.
The Flying Nun - ears up! (see pictorial here).
Crazy dog - occurs especially after baths, runs wildly to and fro.
Bucking Bronco - occurs during Crazy dog phase; begins to buck.
* - my favorite
