Looking for a good compilation album of 20's, 30's and 40's and even 50's music?

Rather than an album, you should listen to some online radio that will play a varitey of tunes for you to listen to and pick ones that you like best.

To start off, check out Yehoodi Radio:

http://www.yehoodi.com/show/radio

It's swing music selected by swing dancers!

You should also check out this Podcast:

http://www.yehoodi.com/show/heymisterjesse

Also swing music for swing dancing.

If you want to talk about, or read other people opinions on, swing music, then is is the best website:

http://www.swingdjs.com/

You can also download original swing music for free on this website:

http://www.jazz-on-line.com/

They are digital copies taken off of 78 records. There's a good collection on there. Use their search feature

There's also lots of general online services for online music such as Pandora, Spotify, Grooveshark, etc. But you also have to know where to start.

I'll recommend you start with the great big band leaders:

Count Basie

Benny Goodman

Artie Shaw

Chick Webb

Duke Ellington

Cab Calloway

Tommy Dorsey

Jimmy Dorsey

(just to name a few)

You can also check out some small combo swing bands like:

Nat King Cole Trio

Cats and the Fiddle

The Three Peppers

Benny Goodman Sextet

Earl Hines

Fats Waller

(etc.)

Anyway, I hope that helps! I hope you also take up swing dancing as well, since you like the music so much. :-)