Here is one:

Commander: U.S. Caence Air force cadence i count candence count candence count
Flight: U
Commander: I can't hear you
Flight: S
Commander: Little bit louder
Flight: A
Commander: lets get fired up
Flight: F
Commander: all together now
Flight: U.S.A.F. UNITED STATES AIRFORCE
Commander: your left, your left, your left, your left is right, your right is left
Flight: AIR FORCE
Commander: your left, your left, your left, your left is right, your right is left
Flight: AIR FORCE

Tell Momma I won't come home
'Till I've hit every drop zone
If my bombs should miss target
I'll just say there's no sure bet
If the flames do not bellow
Drop smoke flares colored yellow
Sound off one two
Sound off three four
Sound off one two three four
One! Two! Three! Four!

more...

Lonnie Courtney Clay

this was probably the corniest we had

hip hop lolly pop let me hear your left foot drop
(cadets stomp left foot)
That sounds mighty fine let me hear it three more times
(Cadets stomp left foot three times)

I am an officer in FL-031 and this is a jody that we commonly use... Hope it comes in handy! It is all started on the left foot and the group responds on the left foot.

CommanderGroup

Count to the left and count ca-dence count
One
I can't he-ar you
Two
A little bit louder now
Three
Make me proud now
Four
All to-gether now
One. Two. Three. Four. Reserve Officer Training Corps (each word on each foot consecutively)
Hoorah!
Hoorah!
Hoorah!
Hoorah!
Hoorah!
Hoorah!

Having looked through a bunch of posts in this thread, I wondered why they were all so clean. It seems the forum rules require it, and today's military has become PC.

This one is from USAF Basic Training. A "rainbow" is a new recruit who has only been issued a PT shirt and is still wearing civvy trousers & shoes. The next cadence is sung by squadrons (who have full issue and have washed it at least once) passing a rainbow squadron.

TI: Rainbow, rainbow, don't be blue.
Squadron: (repeat)
TI: I was once a rainbow too.
Squadron: (repeat)
TI: Sound off.
S: one, two.
S: three, four.
TI: Bring it on down now.
S: one, two (on Lefts; (rapid L/R) three, four!

There were several variations on this one:
I don't know, but I've been told.
Eskimo p***y is mighty cold.

There were a bunch of Jody's too.

birdy birdy in the sky ( flight repeats)
drop a little white wash in my eye ( flight repeat)
im no sissy i wont cry ( flight repeats)
im just glad that cows dont fly ( flight repeats)
sound off ( flight: 1 2)
sound again ( flight: 3 4)
break it on down now ( flight : 1 2 3 4 1 2 air force!)

are you motivated (flight: motivated motivated motivated sir)
are you dedicated (flight: dedicated dedicated dedicated sir)
are you fired up (flight: fired up fired up fired up sir motivate dedicated fired up sir! you check us out you check us out swoo! { when saying swoo you do the burning})

Freedom’s not Free (Air Force Marching Cadence)

Some would say Freedom is free,
But I tend to disagree.
Some say war can be won,
Thru the bullet of a gun.
Once was blind now I see
1st Sgt. got me on my knees,
On that day in September
I will always remember,
Hold your head, hold it high
U.S. Airmen marching by.