Robbery, Assault and Battery
“Robbery, Assault and Battery” - Genesis
Covers murder and theft, at least. Prostitution, arguably. Rape, arson, and probably a few others, depending on the version.
And a crime not yet covered…
Necrophilia:
Cold Ethyl - Alice Cooper
I Love The Dead - Alice Cooper
Dead Girls - Voltaire
UNDEAD necrophilia:
Zombie Prostitute - Voltaire
Night of the Loving Dead - Lordi
Murder:
“Tom Dooley” - folksong
…and probably hundreds more
“Ride Like The Wind” by Christopher Cross
Billy Joel did one about Billy the Kid, I think…
All excellent. Love the Tom Lehrer and the Muppets.
Murder:
“Cocaine Blues” - Johnny Cash (also drug abuse)
“Delia’s Gone” - Johnny Cash
“Rum to Whiskey” - Murder City Devils
“Hey Joe” - Jimi Hendrix Experience
“Ohio” - Crosby, Stills, Nash & Young
Killing of people by freezing them to death; cannibalism - The Candy Machine by Zager & Evans.
From “Chicago”:
*Cell Block Tango
When You’re Good to Mama
We Both Reached for the Gun
*
And about half the songs from “Sweeney Todd.”
Capital Murder:
“The Road Goes on Forever,” Robert Earl Keen
Burglary, Assault with a Deadly Weapon and/or Murder:
“Take the Money and Run” - Steve Miller Band
Apparently I need to give Zager & Evans a second look.
Yes, their songs may on the surface seem like typical late-'60s psychedelic-pop, but the lyrics are ridiculously gruesome (when they’re not simply ridiculous.)
Cannibalism:
The Buoys- Timothy. Written by Rupert Holmes, aka the Pina Colada song guy.
Child killin’:
Violent Femmes- Country Death Song
Every song on Nick Cave and the Bad Seeds’ Murder Ballads
Nick Cave’s “Idiot Prayer” seems to be about a man being executed for murdering his wife or girlfriend
Rats, missed the edit window–I linked to the edited version of Gilmour’s* Murder.* The full-length version (with his great guitar solo) is here.
Lordy, folk music is full of them. Tom Dooley has already been mentioned. How about Long Black Veil, Flora (the Lily of the West), and Banks of the Ohio?
Murder
With a Gun - Steely Dan
Lonesome Death of Hattie Carroll - Bob Dylan
Matty Groves, Long Black Veil, Lily of the West and a zillion other traditional folk songs and Child ballads
Prostitution
Raised on Robbery - Joni Mitchell
Easy Money - Rickie Lee Jones
Psycho killers
Excitable Boy - Warren Zevon
Angie Baby - Helen Reddy
Smuggling
Treetop Flyer - Steven Stills
Smuggler’s Blues - Glenn Frey
Coming Into Los Angeles - Arlo Guthrie
oh, …and littering
Alice’s Restaurant - Arlo Guthrie
Dammit! Once again, you take the words from my mouth.
Don’t change! 
Insane murderer
Aisha by Death in Vegas
Damage I’ve done - Heads
Or you can go to the source, same as the folkies of yore: Anthology of American Folk Music - Wikipedia
And creating a nuisance.