“I Never Talk To Strangers,” a duet between Bette Midler and Tom Waits on her Broken Blossoms album is one of my favorites. Tom Waits also wrote the song.
“Old City Bar” - Trans-Siberian Orchestra
(We Ain’t Going) “Home Alone Tonight” by Luke Bryan and Karen Fairchild
This one tugs at the heartstrings. When the Smoke Clears by Due West.
This one is just a rollicking good time, TROUBLE by Travis Tritt.
Tom Waits has been name-checked multiple times already, but without his absolute best bar song, in my humble opinion: A Sight for Sore Eyes. I dare you not to love that song - it’s got the word “palookas” in it, for gods’ sake!
That’s the one I was just trying to remember. Also “Came Here to Forget” by Blake Shelton, which is the same song but released a couple months later and not as good.
“Half Empty” - Old Dominion
“I Don’t Know About You” - Chris Lane
Well, I’m having the impression that half of the songs posted are country songs, and the other half Tom Waits songs. May there be a pattern? 
Slim Dusty
A Pub With No Beer
Three Rivers Hotel
Mad Jack’s Cockatoo
Joe Maguire’s Pub
Pay Day At The Pub
G’day Blue
Here’s the original. Jake and Elwood stayed pretty close to it.
Or measures will surely be involved… 
[spoiler]Probably a pun for musicians…
David Olney is one of the best little-known songwriters around.
His “Barrymore Remembers” fits this thread.
“Brandy (You’re a Fine Girl)” takes place in a bar, they just talk about sailing and the sea.
Ok, I rechecked the lyrics and turns out Brandy walks home in the last verse. 
So instead I submit Paralyzer by Finger Eleven, unless a club != a bar, in which case I got nothing
Les Miserables has two really good ones: The ABC Cafe/Red and Black and Empty Chairs at Empty Tables.
Al Stewart Modern Times
George Strait - The Chair
“Dive Bar” by Garth Brooks and Blake Shelton
Nick Cave & the Bad Seeds - O’Malley’s Bar. It’s not the kind of bar you want to be in, however. Edit: I guess the very end takes place in a car.
Does “Picture Postcards from L.A.” by Joshua Kadison qualify?
OK, Tom Waits has been mentioned several time…
My Fave, used to play it when I was a closing bartender; Closing Time