Most of the original horror movies from the east that got a horrible remake in the states are pretty good. Premonition, Ju-on (The Grudge), A Tale of Two Sisters (The Uninvited), The Eye, and One Missed Call are all very good, just not the Hollywood trash remakes.
Pulse is a fucking awesome movie that is both slightly scary and horribly depressing and what Hollywood did to it should require everyone involved in making it to be shot in the face live on TV along with a lengthy apology sent to the creators of the original.
On this side of the pond though...
Re-Animator, its a bit more silly and less horror, but its tied for my favorite movie ever
Dead Alive (or Braindead outside of the states), John Carpenter's The Thing, Alien, A Nightmare on Elm Street (its remake wasn't horrible), Friday the 13th (its remake.... JASON DOESN'T FUCKING RUN EVER, EVER, EVER, EVER.. assholes)
but for stuff a bit more modern
Ginger Snaps 1 and 2
Slither
Event Horizon
Trick R Treat
Final Destination 1 and 5
Drag Me to Hell
Session 9
The Devil's Backbone
several episodes of Master's of Horror: Incident On and Off a Mountain Road, Cigarette Burns, Imprint, Jenifer