Here are my ramblings based on what's been mentioned so far.
No one's mentioned The Fly yet. The original is watchable but Cronenberg's remake is excellent.
On the subject of Evil Dead II being a remake of The Evil Dead, from IMDb:
Often considered to be a remake of The Evil
Dead (1981); however, this is not accurate. The rights to show scenes from the original could not be obtained to re-cap what happened, so the beginning was remade to explain how Ash got to the cabin, etc.
http://www.imdb.com/title/tt0092991/trivia?item=tr0723113
The Thing from 2011 was a prequel rather than a remake of Carpenter's 1982 The Thing.
I quite like the term "reboot". I use it to mean a film based on an existing franchise with no connection to the originals and with a mostly new story. I use "remake" to mean a retelling of an existing story.