Here are some of my favorites. Feel free to add to the list.
Red Columbias
Benny Goodman:
Honeysuckle Rose
Why Don't You Do Right
Let's Dance
Mission To Moscow
Anything else with Peggy Lee
Woody Herman
Atlanta, G.A.
Count Basie
Ride On / It's Sand, Man!
Harry James
All Or Nothing At All (1950s reissue- good luck finding an original 1939 "Jazz Masterworks pressing!)
I've Heard That Song Before
Prince Charming
Who told you I cared? (Sinatra- usually found as '50s reissue)
Decca
Jimmy Dorsey
Perfidia
Tangerine
They're Either Too Young Or Too Old
Guy Lombardo
Managua, Nicaragua
Charlie Barnet
Skyliner
Glenn Miller
Moonlight Bay- this was reissued in the black label era
Woody Herman
Laughing Boy Blues
Blues In The Night
Bob Crosby
The "Shakespeare in Swing" sides are quite interesting, issued as a 2 record set
Bluebird
Many 1920s Victor 38000 "Race" series reissues
Artie Shaw
Any Old Time w/ Billie Holiday. Early issues state "Art" Shaw and "Billy" Holiday. Earliest are on Staff label
Glenn Miller
In The Mood (of course!)
Kay Kyser
Collegiate Fanny
Charlie Barnet
"Cherokee"
"The Wrong Idea" (hilarious spoof on Sammy Kaye as "Swing and Sweat with Charlie Barnet", supposedly Kaye wanted to "kill" Barnet over it)
OKeh (purple label)
Benny Goodman:
Jersey Bounce
All others with Peggy Lee
Victor
Benny Goodman
Just about any- even RCA reissues- these were Benny's "breakout" sides, lots with Fletcher Henderson arrangements, and are quite good!
Tommy Dorsey
I've Got a Note
Satan Takes A Holiday
Jammin'
Josephine/ If the Man In The Moon Were A Coon (racist lyrics and Jack Leonard sounds a little embarrassed, but a great arrangement with mercifully short vocal. Knowing Tommy's feelings about racist BS I'm surprised he recorded it!)
Swing Time Up In Harlem/ Swing High
Will You Still Be Mine? (Connie Haines)
Yes, Indeed! (Jo Stafford and Sy Oliver vocal- great record and pushes the contemporary racial "envelope" with a black guy singing with a white girl! Radical for 1941)
All sides with Sinatra. Though later ones with the added string section can be sappy, it's still Frank!
Well, Git It!
Opus One
At The Fat Man's (w/ Charlie Shavers)
Sweet Eileen
I Ought To Know More About You
Artie Shaw
April In Paris
Alone Together
King For A Day
Who's Excited
What Is There To Say?
Don't Fall Asleep
Gloomy Sunday
Cross Your Heart/ Summit Ridge Drive
I Can't Get Started
A Foggy Day
That's all I can think of off the top of my head on short notice.
Who else wants to play?