Honestly, I think the shows and movies and that need a remake the most, are the ones that failed horribly. Because they're the ones that need the second chance the most.
You don't remake The Thing, it's a classic that would be difficult if not impossible to improve upon. But you do remake The Thing from Another World because it was crappy and cheesy.
It's one of the reasons why all of the 1980s remakes of 1950s movies are so brilliant, The Fly and The Blob being two good examples. A bit of a shame that Invasion of the Body Snatchers was remade in the 70s though (but that's just my personal preferences talking there). :(
So yeah, when thinking of things that could be remade, I think it's best to think of things that aren't good, but maybe had potential. The Black Cauldron immediately comes to mind, but that is getting a remake.