As I promised ;)
I don't know which way is better to list all of them, so I just will write a name of a track and a video I've heard it in.

Michael's Vsauce

1. Ice Houses by Richard Lacy
   from What's The Brightest Thing In the Universe? and also later in the same video

2. Book Of Secrets by David O'Brien
   from What's The Brightest Thing In the Universe?
   and How Many Things Are There?

3. Soft Focus Bossa by Paul Mottram
   from What Does Human Taste Like? intro

4. From Another World by Chris Blackwell
   from What Does Human Taste Like?

5. Rising Fear by David O'Brien
   from What Does Human Taste Like?
   and Why Are Things Creepy? intro

6. World Of Dreams by Bob Bradley
   from Why Are Things Creepy?
   and last words

7. Conversation by Bob Bradley
   from Why Are Things Creepy?
   and What Is The Speed of Dark? Intro
   and Messages For The Future

8. Ghost Train by David O'Brien
   from Intro of How Many Things Are There?

9. Algorhythm by Barrie Gledden
   from What Is The Earth Worth? Intro

10. Prophecy by Dan Skinner
    from What Is The Speed of Dark? Intro

11. The Plan by Paul Mottram
    from What Is The Speed of Dark?

12. Heavy Heart by Christian Marsac
    from What Is The Speed of Dark? Outro

13. Eye Contact by Richard Lacy
    from How To Count Past Infinity

14. Breaking The Code by Sam Wedgwood
    from How To Count Past Infinity

15. Digital Heartbeat by Daniel Gautreau
    from How To Count Past Infinity

16. Crest Of A Wave by Jason Pedder
    from Supertasks

17. Airwaves by Mark Denis
    from Supertasks

18. Expanse by David O'Brien
    from What If The Earth Stopped Spinning?

19. American Tragedy by David O'Brien
    from last words

20. Mysterons by David O'Brien
    from Messages For The Future

21. Poker Face by Matt Hill
    from Messages For The Future

22. "Midnight Sound" by Gareth Johnson
    from Where Do Deleted Files Go?

23. Walkabout by Terry Devine-King has been used in various videos but I can't recall any exact ones, and I'm kinda lazy to look for them..

The same can be said for the following:
24. Vampire Strut by Bob Bradley
25. Dew Drops by David O'Brien
26. Elevator by David O'Brien

Kevin's Vsauce2

1. Has been used in outros

2. Block Out The Sun by Paul Ressel
   from The Line Between People And Pets Outro

Jake's Vsauce3

1. Unknown Soldier by Philip Sheppard
   Outro song from Could You Live Forever?

2. I think I've heard this piece of Lakme opera in one of his videos///

3. Hatching by Jeff Lardner:
   Has been used in both #1 and #3 of Extreme Science

4. Dream Oasis by Paul Mottram
   from 4 Logical Paradoxes!!

5. Thunder Approaches by Alex Arcoleo
   from 4 Logical Paradoxes!!

6. Sniper by Alex Arcoleo
   from Could You Be Iron Man?

7. Intense Dark by Barrie Gledden
   from Could You Be Iron Man?

And of course from What if the World Ended?:
1. Intro music Electric Tears by Barrie Gledden
2. Drifting By by Richard Lacy
3. Dead Sea by Richard Lacy
4. Universal by Richard Lacy
5. Crest Of A Wave by Jason Pedder
6. Sagan by Richard Lacy
7. Hold On Gold by Terry Devine-King

• Oh, and also this one! It has been in one of Jake's vlogs

That's all I've managed to gather so far. I didn't include those by Jake Chudnow, for the obvious reason that everyone can find them on his soundcloud, and they are found in practically every Vsauce video.