Below is the YouTube of an unfinished version of "Now and Then," a song which is complete at this point and the remaining Beatles might release in the not-so-distant future. Even in unpolished form, it's a very compelling track: haunting, heartfelt, and unique (notice the absence of a conventional chorus; basically just three distinct verses). And, on certain levels, it's of a piece sonically with "Free as a Bird" and "Real Love," both of which also came out long after The Beatles disbanded. I know many hope that "Now and Then" will soon officially join the company of those two songs.
"Now and Then"
(If the video is removed, go here.)
P.S. It's interesting that parts of "Sun King" make an appearance near the end of the song.