For anyone who cares, here is the complete Soundtrack listing from imdb. I think they're all in order too.
"Rags to Riches"
Written by Jerry Ross (I) and Richard Adler
Performed by Tony Bennett (I)
Courtesy of CBS Records, Music Licensing Department
"Can't We Be Sweehearts"
Written by Morris Levy and Herbert Cox
Performed by The Cleftones
Courtesy of Rhino Records
"Hearts of Stone"
Written by Eddie Ray and Rudy Jackson
Performed by Otis Williams and The Charms
Courtesy of G.M.L., Inc. by Arrangement with Celebrity Licensing Inc.
"Sincerely"
Written by Harvey Fuqua and Alan Freed
Performed by The Moonglows
Courtesy of MCA Records
"Firenze Sogna"
Written by Giuseppe di Stefano
Performed by Giuseppe di Stefano
Courtesy of London Records, a Division of PolyGram Records, Inc.
"Speedo"
Written by Esther Navarro
Performed by The Cadillacs
Courtesy of Rhino Records
"Parlami d'amore Mariu"
Written by Enrico Neri and C.A. Bixio
Performed by Giuseppe di Stefano
Courtesy of London Records, a Division of PolyGram Records, Inc.
"Stardust"
Written by Hoagy Carmichael and Mitchell Parish
Performed by Billy Ward and His Dominoes
Courtesy of Billy Ward c/o Original Sound Entertainment
"This World We Live in"
("Il cielo un una stanza")
Written by Toang, Mogal and Raye
Performed by Mina
Courtesy of Shad/Mainstream Records
by Arrangement with Celebrity Licensing Inc.
"Playboy"
Written by Brian Holland (I), Robert Baleman and William Stevenson
Performed by The Marvellettes
Courtesy of Motown Record Company, L.P.
"It's Not for Me to Say"
Music by Robert Allen
Lyrics by Al Stillman
Performed by Johnny Mathis
Courtesy of CBS Records, Music Licensing Derpartment
"I Will Follow Him"
("Chariot")
Written by Norman Gimbel, Arthur Altman, J.W. Stole and Del Roma
Performed by Betty Curtis
Courtesy of CGD Records
"Then He Kissed Me"
Written by Phil Spector, Ellie Greenwich and Jeff Barry (I)
Performed by The Crystals
Courtesy of Phil Spector Records Inc. by Arrangement with ABKCO Records
"Look in My Eyes"
Written by Richard Barrett
Performed by the Chantels
Courtesy of Rhino Records
"Roses Are Red"
Written by Al Byron and Paul Evans
Produced by Bob Gaudio
Performed by Bobby Vinton
Courtesy of Curb Records
"Life Is But a Dream"
Written by Raul Cita and Hy Weiss
Performed by The Harptones
Courtesy of Old Town Records - Paradise Records, Inc.
"Leader of the Pack"
Written by George Morton, Jeff Barry (I) and Ellie Greenwich
Performed by The Shangri-Las
Courtesy of Sun Entertainment c/o Original Sound Entertainment
"Toot, Toot, Tootsie Goodbye"
Written by Ernie Erdman, Ted Florilo and Gus Khan
"Happy Birthday to You"
Written by Mildred J. Hill and Patty S. Hill
"Ain't That a Kick in the Head"
Written by Sammy Cahn and Jimmy Van Heusen
Performed by Dean Martin
Courtesy of Capitol Records by Arrangement with CEMA Special Markets
"He's Sure the Boy I Love"
Written by Barry Mann and Cynthia Well
Performed by the Crystals
Courtesy of Phil Spector Records Inc. by Arrangement with ABKCO Records
"Atlantis"
Written by Donovan Leitch
Performed by Donovan
Courtesy of CBS Records, Music Licensing Department
"Pretend You Don't See Her"
Written by Steve Allen
Performed by Jerry Vale
Courtesy of CBS Records, Music Licensing Department
"Remember (Walkin' in the Sand)"
Written by George Morton
Performed by the Shangri-Las
Courtesy of Sun Entertainment c/o Original Sound Entertainment
"Baby I Love You"
Written by Ronny Shannon
Performed by Aretha Franklin
Courtesy of Atlantic Recording Corporation
by Arrangement with Warner Special Products
"Beyond the Sea"
Written by Jack Lawrence (II) and Charles Trenet
Performed by Bobby Darin
Courtesy of Atlantic Recording Corporation
by Arrangement with Warner Special Products
"The Boulevard of Broken Dreams"
Written by Al Dubin and Harry Warren
Performed by Tony Bennett
Courtesy of CBS Records, Music Licensing Department
"Gimme Shelter"
Written by Mick Jagger and Keith Richards (II)
Performed by The Rolling Stones
By Arrangment with ABKCO Music & Records, Inc.
"Wives and Lovers"
Written by Burt Bacharach and Hal David (II)
Performed by Jack Jones
Courtesy of MCA Records
"Monkey Man"
Written by Mick Jagger and Keith Richards (II)
Performed by The Rolling Stones
By Arrangment with ABKCO Music & Records, Inc.
"Frosty the Snow Man"
Written by Steven Nelson and Jack Rollins
Performed by The Ronettes
Courtesy of Phil Spector Records Inc. by Arrangement with ABKCO Records
"Christmas (Baby Please Come Home)"
Written by Phil Spector, Ellie Greenwich and Jeff Barry (I)
Performed by Darlene Love
Courtesy of Phil Spector Records Inc. by Arrangement with ABKCO Records
"Bells of St. Marys"
Written by Douglas Furber and Emmett Adams
Performed by The Drifters
Courtesy of Atlantic Recording Corporation
by Arrangement with Warner Special Products
"Unchained Melody"
Written by Hy Zarel and Alex North
Performed by Vito and The Salutations
Courtesy of Arista Records
"Danny Boy"
Written by Frederick E. Weatherly
"Sunshine of Your Love"
Written by Jack Bruce, Peter Brown and Eric Clapton
Performed by The Cream
Courtesy of PolyGram Special Products
a Division of PolyGram Records, Inc.
"Layla"
Written by Eric Clapton and Jim Gordon
Performed by Derek and The Dominos
Courtesy of PolyGram Special Products
a Division of PolyGram Records, Inc.
"Jump into the Fire"
Written by Harry Nilsson
Performed by Harry Nilsson
Courtesy of RCA Records
"Memo from Turner"
Written by Mick Jagger and Keith Richards (II)
Performed by The Rolling Stones
By Arrangment with ABKCO Music & Records, Inc.
"The Magic Bus"
Written by Peter Townshand
Performed by The Who
Courtesy of MCA Records
"What Is Life"
Written by George Harrison
Performed by George Harrison
Courtesy of Apple Records
Courtesy of Apple Records by Arrangement with CEMA Special Markets
"Mannish Boy"
Written by McKinley Morganfield, Mel London and Elias McDaniel
Performed by Muddy Waters
Courtesy of CBS Records, Music Licensing Department
"My Way"
Written by Claude Francois, Jacques Fleveaux and Paul Anka
Produced by Steve Jones
Performed by Sid Vicious
Courtesy of Virgin Records Limited/Glitterbest, Inc.