"Greatest Hits", "Anthologies", and "Collections" (Gold, Essential, Platinum, or otherwise) are not allowed on desert islands. Compilations and Box Sets are out too. They drowned. Live albums are very suspect.
Also, there are no ipods or ipads on the Island—only a record player with two big speakers purchased from a van in the back of a Safeway parking lot. You use the speakers as a raft to save you from the wreckage of your submarine, and to escape Charles Widmore. Unfortunately, you had to use Abbey Road and Revolver as paddles.
So, here are the records that made it:
Rumours –Fleetwood Mac
Car Wheels on A Gravel Road-Lucinda Williams
Full Moon Fever-Tom Petty
Fox Confessor Brings the Flood-Neko Case
Running On Empty-Jackson Browne
Blood On The Tracks-Bob Dylan
Pet Sounds-The Beach Boys
Teaser and the Firecat-Cat Stevens
Note: I may or may not have a second desert island, just like they had in Lost.