For starters, any ballad by Tom Waits.
For example:
On The Nickel
The Fall Of Troy
Diamond In Your Mind
Ruby’s Arms
Time
Tom Traubert’s Blues
Georgia Lee
Also lots and lots of Irish songs.
For example:
The Dubliners - Preab San Ol
The Dubliners - The Mero
The Dubliners - Monto
What are your best/favourite drunken songs?
Ahem.
Louie, Louie! Ohhh, no, me got to go!
Ay ay ay ay ay ay
Louie, Louie! Ohhno, me something else!
Ayay ay ay aya y
Louie, Louie! Ohhh hold on…
throws back a shot
Oooh! Good topic.
I am very fond of Great Big Sea’s The Night Pat Murphy Died.
I hate the musical Brigadoon, but the song My Mother’s Wedding Day is great fun.
Heather Alexander’s Branigan’s Special Ale is also grand fun.
I know I have more of this sort of song, but I’m not home at the moment and I can’t seem to bring them to mind, now.
Come On Eileen by Dexy’s Midnight Runners. Get yourself drunk and give it a try; I guarantee you’ll be whirling like a dervish or marching up and down your living room in no time.
You never called me by my name - David Allen Coe (mistakenly referred to as “you don’t have to call me Darlin”
I love Great Big Sea’s versions of Newfoundland folk songs. In fact they’re going on my playlist now! 
Chumbawumba!
Dropkick Murphys!
Flogging Molly!
Beat me to it dammit.
Family Tradition by Hank Williams, Jr.
Merry Christmas From The Family by Robert Earl Keen
Lost Weekend – The Beat Farmers
FREE BIRD!!!
Actually that’s just fun to yell when you’re drunk.
Made famous in the movie Jaws.
The Scotsman is a classic. And The Holy Grail of Irish Drinking Songs is definately on my add-to-iTunes-someday list.
Spirit of the West - Home for a Rest
Canadian University Party Anthem!
Tyr’s cover of The Wild Rover is pretty fantastic.
I just hope nobody mentions “Sweet Caroline.” There’s nothing worse than hearing a bunch of drunks trying to imitate that “BUM Bum bum” line.
Cisco Kid.
At the chorus everyone is supposed to join in drunken shouting…
“Ride…Ride…Ride”