There's a box of 4 cd's available, containing every song in this subject. Bootlegzone gives a lot of information on this topic. The text below is taken from that site.
http://www.bootlegzone.com/album.php?name=cd490351§ion=1A collection of songs that were never properly recorded by The Beatles or their members.
All dates are dubious (taken from booklet) and probabaly refer to the day the songs were released.
Liner notes:
One of the passions of a true Beatles fan who wants everything, is to collect all the songs ever written (or co-written) by all of the 4 Beatles. Such a daunting (and expensive!) task has just been made instantly obtainable with this 4 CD set, which, as an added bonus, includes the Beatles' own versions of many of these great songs.
What becomes obvious after only half of the first disc, is that if The Beatles chosen to record some of these songs officially as a complete album, it would have been a monster hit, for example, on the first disc (which features songs given away while the Beatles were still together) there are no less than 11 top ten hits - a remarkable feat from a group already blessed with "Guaranteed Hits" status.
The only known (and deliberate) omission from the set is (apart from "Leave It") all of the tracks from Mike McCartney's Mc Gear album, which is now freely available on CD. We've still included, however, the FAB 45 "Leave It", "Sweet Baby" (not on the LP or re-issued CD) and the non-LP 45 "Dance the Do" (in it's original form - the CD version is a dramatically different recent re-mix)
The second disc continues the story into the early 70'S, including one-off items like George's "Sing One For The Lord" only available on Billy Prestons otherwise unspectacular "Encouraging Words" Apple LP, early mixes of the various songs Ringo was given for his "Ringo" LP in 1973, the very rare McCartney penned "4th July" (for John Christie), Billy Lawrie's "Rock and Roller (co-written by Ringo) and Peggy Lee's "Lets Love" which stands to this day one of McCartney's finest songs.
Disc three takes us through to the recent McCartney/Costello hit "Veronica" and includes both Gary Moore and Eric Clapton's versions of George's "That Kind Of Woman" (Clearly Eric wins!) also included on disc 3, McCartney's "Mine For Me" (Rod Stewart), Giddy (Roger Daltrey), On The Wings Of A Nightengale" (Everly Bros), "Honorary Consul" theme (John Williams) and the very rare "New Moon Over Jamaica" (Johnny Cash) which also features Paul singing duet lead vocal.
This set will also satisfy those "semi-fans" who don't wish to purchase Ringo's output over the years, by including all songs given to him by the other 3 Beatles: e.g. "Cookin" (John), "Pure Gold" (Paul), "I'll Still Love You" (George) plus the many others as well.
Disc 4 concludes the set with as many of The Beatles own versions of these songs as have ever been heard till now, for example, we have sourced the acetates of one-off demo's of "Bad To Me", "One and One Is Two", "Step Inside Love", "Goodbye" and "On the Wings Of A Nightingale", a total of 20 performances of the 68 songs given away are included on this the final CD in the set. As is normal, it is our quest to make all of our releases maximum value for money, so we've added 30 bonus tracks/excerpts/oddities and the many mono/stereo differences which for anyone but the absolute die-hard fan will surely offer some unknown treasures. For example, how many of you knew that the mono "Matchbox" has a totally different guitar solo to the stereo version?
This 4 CD set is a "dream come true" for collectors and will be recorded as a "must have" for all Beatles fans.