I’ve never served myself, but I do like military songs and cadences. I thinks it’s hard to beat the Ranger’s ‘Blood Upon the Risers’ (‘Glory Glory, What a Hellava Way to Die’)
Holy shit that songs haunting.
Here’s a youtube of it:
Anybody else have a favorite?
Anything but the Infantry March. I am partial to The Thunderer and the Washington Post. I would like to hear Sousa’s Under the Double Eagle.
Sung to the tune of The Halls of Montezuma a British Airborne song.
We have a nasty reputation for seducing little boys
For raping old age pensioners
And breaking Crap Hats toys
We are the arseholes of the nation
We are the cunts you never see
We’re a bunch of loud mouthed bastards
We are the airborne infantry!
I do like The Halls of Montezuma. Seems to hearken back to a more spirited, purposeful time. Course I don’t really know many service songs at all.
There she was, just a- walkin’ down the street . . .
Does this count? It’s from Girl Scout Camp…
Left, left, left right left.
Left, left, left right left.
I left my wife and forty-six children home in the kitchen with only one hamburger
left, left, left right left…
Three by Kipling, which I’ve heard set to marchable martial-style music by [[url=Black and White Party Attire and Hosting Tips]“Boots”](]Leslie Fish:[/url)
Sorry, Leslie Fish.
Blood on the Risers was (I shit you not) the first song I ever learned to sing. Why, yes, my father was in the 82nd Airborne. Why do you ask?
The 82nd Airborne All-American Choir used to come to my grade school every year and perform a concert. Other than saying “heckuva”, they did Blood on the Risers just as in the YouTube clip cited in the OP – blood splattering and all. In the final verse, as they described the remains of the poor rookie scattered all over the landing zone, various members of the chorus burst into hammy sobs and pantomimed picking up body parts from the ground. And 500 school kids screamed with glee and nearly wet their collective pants from laughing.
I loved growing up in the Army.
Not quite what you were looking for - but I like the music for “Eternal Father, Strong to Save” (the Navy Hymn).
From a great movie depicting one of the greatest bad ass moments in all military history.
Men of Harlech wasn’t the actual anthem of the 24th Reg of foot at the time of Rorke’s Drift but it was soon after.
I can’t get a recording of it, but if the Zulu’s song in response sounded anything like the movie I would have shit my pants as well.
It will be sung at my funeral. Surely a great military song, but not a cadence or march.
A few different ones, for me…
•The Minstrel Boy.
•I found the lyrics to this one, awhile back, and thought it was rather gruesomely charming.
Phantom flyers in the sky,
Persian pukes prepare to die,
Rolling in with snake and nape,
Allah creates but we cremate.
North of Tehran, we did go,
When the FAC said from bellow,
‘Hit my smoke, and you will find,
The Arabs there are in a bind.’
Probably incomplete, and/or out of order. Occasionally, to kill an odd moment of time, I tinker with this one to try and update it. (The best rhyme I could come up with for “glass” was “ash.”)
•Any number of Marine Corps running cadences—we had the Run to Cadence with the U.S. Marines tape ever since I was a little kid. I think I probably learned “My Grandaddy was a Horse Marine” before “Itsy Bitsy Spider.” 
•“Pack Up Your Troubles (In Your Old Kit Bag)” Anyone else imagine Snoop—er, the World War I Flying Ace, just for a second, when hearing this one?
(Not sure of the OP: cadences/jody calls, marching songs, marches?) Anyway, the highlighted links are to streaming video
The Germans have so many of them, the vast majority of which are too “oompha-oompha” for my tastes, but I do like :
Unser Rommel (nice intro) and Panzerleid “has a nice beat and you can invade Poland to it.”
The French have some peppy tunes, although the Foreign Legion’s are either dirge-like to match their 80-pace a minute march, or are borrowed for Nazi songs (more on that topic than anyone is interested in knowing).
The Austrians gave us one of the most fun marches, so much so that we could forget what a nasty empire they ran.
The Russians have always been singing, marching fools, Some of my favories are
My litle doorstep (which Stravinski used in the ballet “Petruschka.”) and “Off We Go”
Further east, let’s not forget that the Persian & Turks invented military music (Inspiring to march to? Maybe, but not necessarily sideways.)
World War One was the last great singing war we’re likely to have until World War Four, and many of its best songs were used in the musical & film Oh What a Lovely War. But for a short run-thorugh, there was an entire episode of CBS’s 1964 World War One devoted to them.
When I was a kid my grandpa (who was in the Army, in the Korean War) always sang these two songs:
“You’re in the Army now! You’re in the Army now!” That’s all I can remember of it.
“It’s time to get up, it’s time to get up, it’s time to get up in the morning!” (To the tune of Reveille.) That one annoyed the hell out of me because I hated being woken up in the morning.
I would have to say my favorite ones are the ones they sing in Full Metal Jacket.
Back in the late 70’s, when my husband was in the Army, there was a cadence song that featured various people from the Bible. I only remember a few phrases:
Jesus led a 12 man A-team
Noah led a water mission
David was a small-arms expert
There was a chorus between these phrases of some kind but I don’t remember any more. Does anybody else remember this?
I would love to find this old Cold War one. A sergeant in my company was the only one I heard do it. It was a running cadence to the tune of Davy Crokett. I only remember the one line, “We fired our TOWs and the Commies kept a commin.”
You’re not behind a plow! So dig that ditch, you son of a bitch, you’re in the Army now!
That sounds more like Johnny’ Horton’s “The Battle of New Orleans”.
Do you want running or marching?
My best cadence for running is:
*C-130 rolling down the strip
64 Paratroopers, one way trip
Mission top secret destination unknown
Don’t even care if they ever coming home
Stand up, Hook up shuffle to the door
Jump right out and you count to four
If my main don’t open wide
I got a reserve by my side
If that one should fail me, too
Look out below 'cause I’m coming through
Bury me on the Russian front
Bury me with a Russian…rifle 
*
For marching:
[chorus]
*Hail, hail, lock and load
The sound of the roters
Is loud and cold
But I was always redy to go
So early in the morning[/chorus]
My daddy said I was a fool
When I requested Airborne School
But I was always ready to go
So early in the morning
[chorus]
They sent me off to eighty duce
A band of killers on the loose
But I was always redy to go
So early in the morning
At 3 am I got the call
Paratrooper get ready to fall
But I was always ready to go
So early in the morning*
There is a lot more, but it is too late to type.
Alas, my favorite is “When Johnny Comes Marching Home,” which I learned in 5th grade when we spent half the year learning Songs of the Revolutionary to the Civil War.