I'm right with you on the way they change things up live. A lot of them never appeared on official live releases, but a bunch of them did end up on official bootlegs, as well as soundboard, radio broadcast and audience bootlegs. Some that come to mind:
the various instrumental jams that appeared throughout the Images and Tour and Music in Progress tours, such as Moon Bubbles, Slow Motion, Bombay Vindaloo and Barfbag
the Another Hand instrumental bridge on the Images and Tour and later tours when The Killing Hand was played
the extended instrumental jam following To Live Forever on 2 of the legs of the Music in Progress tour
the revamped intro to Status Seeker on the North American leg of the Music in Progress tour
the extended jam at the end of Take the Time on the Waking Up the World tour
the Awake Jam on the Waking Up the World tour
the A Crack in the Mirror intro to the Mirror on the Waking Up the World and Touring Into Infinity tours
the revamped version of Caught in a Web - called Caught in Alice's Nine Inch Tool Garden as played on the Fix for 96 and Evening of New Music tours
additional music jam included in Learning to Live on the Fix for 96, Evening of New Music and 20th Anniversary tours
their versions of the Mission: Impossible theme Dr. Evil theme, Thus Spake Zarathustra
the Working Man/By-Tor jam tacked on the end of Take the Time on World Tourbulence
the 2112 Grand Finale tacked on the end of Scarred on World Tourbulence
the warped version of Pull Me Under on World Tourbulence
extended versions of Hollow Years played on the Train of Thought and Progressive Nation 2009 tours
the additions of Pink Floyd and Metallica tracks in Peruvian Skies on the Touring Into Infinity and 20th Anniversary tours
on L@LP, there is an extended jam at the end of Metropolis part 1
several changes to songs during the Images and Words set on the Images, Words and Beyond tour
extended intro to Hell's Kitchen on the Images, Words and Beyond tour
the excerpt of Enter Sandman included in As I Am on the Images, Words and Beyond tour
I'm sure there's more, but those are the ones that come to mind right now.