By far, my favourite is Mr Bungle's "Disco Volante" on vinyl.
It has a hidden track within the 3rd song. If you play the album through you'll never hear it, but if at the start of the 3rd track you search with the needle, you'll find a second groove in which the hidden track will play and drop out of the groove at the end of the 3rd track and continue on with the album!
On the CD, they simply couldn't do it, so the hidden track was tacked onto the end of the 3rd track.