I think the key to remakes is to not remake good movies (or at least, good for their genre), like:
The Manchurian Candidate
The Posiedon Adventure
The Omen
Disturbia/Rear Window
Flight of the Phoenix
The Hills Have Eyes
Miracle on 34th Street
One Missed Call
When a Stranger Calls
The Wicker Man
The Wolfman
The Parent Trap
Death at a Funeral
Those are just the ones that come to mind at the moment. But....on the other hand, there are some incredible remakes out there:
Gone in 60 Seconds
Father of the Bride
Fun with Dick and Jane
Dawn of the Dead
The Ladykillers
Little Shop of Horrors
Meet Joe Black
The Mummy
Munich
Oceans 11
Psycho (guess it depends on the viewer, I really liked it)
Scarface
I think it can really go either way with a couple of soft rules
-The movie should NOT have been considered one of the best movies ever made (posiedon/Manchurian candidate)
-Horror movies are probably a bad idea, but you may pull something out if you don't feel you have to put a Megan Fox look-alike in it
-Don't put Dennis Quaid in it.
-If its an old comedy from the 50s - 60s you could see some real improvement with a remake, as so much of the original value is based on contemporary social norms (father of the bride)
-Give it more than a couple years (death at a funeral)
-If it is heavily dependant on special effects, you could do well with a remake, but be careful (Little Shop of Horrors and Dawn of the Dead, but also the Hills Have Eyes)