- Opening/prologue: uncredited, but styled after Ralph Vaughan Williams' Fantasia on a Theme by Thomas Tallis
- "Love Theme": uncredited (although, I strongly suspect this may be the rumored George Martin work since it does have a lot of similarities to Martin's score for Yellow Submarine)
- Dance of the One Eyes/March of the One-Eyes: uncredited (the "Dance" track sounds a lot like it could be the "Dix Six" jazz band that Richard Williams fronted, plus someone with a violin/fiddle near the end of the cue)
- The really grand music used in several points (like the staircase chase) is Scheherazade by Rimsky-Korsakov
- A short cue during the March of the One Eyes section (up until the shot of the elephants being lowered, later when the Nurse shouts): Mountaineer's Dance/Dance of the Boys - Aram Khatchurian
- The music when The Thief finally gets the golden balls is "I'm Forever Blowing Bubbles"
- A short bit of Tico Tico is played when the witch grabs Tack down
- There's a lot of other original music at various points that's still uncredited. I'd imagine Richard Williams had some hand in composing some of it since he's a musician too.
- I think it's obvious what was added to the shots of the Thief flying and also the Fantasia homage

(a lot of this is from stuff some people pointed out earlier in this massive thread)
I really think tygerbug did a great job with adding music for the latest version, even if doesn't sync as well as the Robert Folk score. The problem with that is the lack of music for deleted footage. Russian Easter Overture just sounds awesome for the war machine destruction, IMO. I'll admit that Robert Folk's score for parts of the war machine destruction is pretty good. The unfortunate comparatively low fidelity of the workprint track makes the sequences with only sound effects can be tiring to the ears. Although, a few sections have surprisingly high quality sound in spots, despite some hiss.