The following is a list exclusively of songs for which studio versions exist in circulation but were never put on an album. I am NOT including those from iTunes' Unreleased & Rare since they are now officially released. There are other unreleased songs that the band solely played live or in soundchecks, or that we know were recorded in studio but which are not in circulation. Can list those if you want.
This is off memory, so apologies for any omissions.
Pre-Boy:
Inside Out
Jack In A Box
Tonight
Trevor
False Prophet
Lost On A Silent Planet
Alone In The Light
The Dream Is Over
(plus numerous unreleased demos of Boy songs)
Post-Boy
Be There (1982)
Untitled UF Instrumental (aka Flicker And Fade, 1984)
Seven 30 second snippets of JT sessions songs (one is Rise Up, two are early versions of Walk To The Water and Race Against Time)
She's A Mystery To Me (1987)
Wild Irish Rose (1988)
The complete songs on Axtung Beibi (1990)
Mercy (2004)
And even though it was just played live, I must not neglect to mention that immortal unreleased U2 epic from 1986 ... yes, I'm talking about WOMANFISH.