Many people have been writing in requesting the soundtrack list of all the music in the game. Here is everything I have found so far. Feel free to add to this in the comments section...

So here you go!

LICENSED
Beyond the Sea - Bobby Darin
If I didn't Care - The Ink Spots
The Best Things in Life are Free - The Ink Spots
Papa Loves Mambo - Perry Como
Bei Mir Bist du Shon - The Andrew Sisters
How Much is that Doggie in the Window? - Patti Page
Brother Can You Spare a Dime? - Bing Crosby
Wrap Your Troubles In Dreams - Bing Crosby
It's Bad for Me - Rosemary Clooney (George Clooney's Aunt)
You're the Top - Cole Porter
Night and Day - Billie Holiday
Nutcracker (Waltz of the Flowers) - Peter Illyich Tchaikovsky
The Party's Over - Judy Holliday
Please Be Kind - Frank Sinatra
Jitterbug Waltz - Fats Waller
It Had to Be You - Danny Thomas
Oh Danny Boy - Mario Lanza
20th Century Blues - Noel Coward
World Weary - Noel Coward
The Party's Over - Noel Coward
God Bless The Child - Billie Holiday
Just Walking In The Rain - Johnnie Ray
La Mer (Beyond the Sea Instrumental) - Django Reinhardt
Wild Little Sisters - ?

ORIGINAL SCORE
BioShock Main Theme (The Ocean on His Shoulders)
Welcome to Rapture
Dr. Steinman
The Docks
The Dash
Step Into My Gardens
Dancers on a String
Cohens Masterpiece
The Engine City
Empty Houses
This is Where They Sleep
All Spiced Up

LIMITED EDITION SOUNDTRACK
Beyond the Sea - Moby, Oscar the Punk Remix
God Bless the Child - Moby, Oscar the Punk Remix
Wild Little Sisters - Moby, Oscar the Punk Remix