I’m cheating because I didn’t see the original Last of the Mohicans movie, but I READ that the remake was better.
Could we get a remake of the OP? 
The recent Oceans 11 remake is way better than the original
The Thomas Crown Affair remake is probably as good as the original although Pierce Brosnan lacks Steve McQueens charisma.
The Magnificent Seven is a remake of Seven Samurai and although it isn’t really better, it is still pretty damn good.
Heat is a remake (with far bigger budget) of an earlier Michael Mann movie (I forget the title) and is far better.
And this probably doesn’t count but Evil Dead II is pretty much a remake of the first one and is far better.
A lot of people seem to thin that His Girl Friday was far superior to the original The Front Page (as well as to subsequent remakes). I still kinda like the original, though.
Most remakes of early silent films are superior – with much greater running length, a greater commitment to following the original story, and the addition of sound (although some will dispute that), you usuually got better flicks. I haven’t seen The Sea Beast, but Moby Dick with a happy ending (!) just sounds weird – and the John Huston/Ray Bradbury/Richard Basehart version was GREAT. Similarly, I’ll take the 1931 Frankenstein or Kenneth Branuagh’s version over the 1910 version, or Cecil B. deMille’s 1956 version of The Ten Commandments over his 1923 version.
And damn, how could I forget that the third version of The Maltese Falcom easily trumps the two earlier ones, or how the 1939 Wizard of Oz is far superior to Larry Semon’s silent version (and, I think, the Baum versions as well).
Most critics prefer Hitchcock’s second take on The Man Who Knew Too Much to his first, I believe.
Stephen King’s The Shining, that was made for TV, was magnitudes better than the Kubrick version.
Are you kidding?
Some of the mentioned films I would place on my list.
Incidentally, take a look at this poster for “L.A. Takedown” - the word “heat” on the poster appears the saem as it does on the posters for "“Heat.”
“Red Dragon” was just as good, IMHO, as “Manhunter.” In the context of remakes, “just as good” is awesome.
“The Lord of the Rings: The Fellowship of the Ring” was a wonderful movie, and we can safely expect the sequels will be just as good. The Ralph Bakshi animated version makes Baby Jesus cry.
“Insomnia” was every bit as good as its Norwegian predecessor, and maybe a little better.
I’m glad to see that someone besides myself, norinew, believes about the Shining.
The first one wasn’t even remotely close to the book (Hallorann dies!), and nothing bothers me as much as a director/writer screwing over a writer’s vision.
msmith, no I’m not kidding! My biggest problem with Kubrik’s is Jack NIcholson. Now, I like Jack Nicholson for some things, but he just wasn’t right for this movie. In the movie, the character is supposed to start off okay, then get crazier and crazier as he is slowly possessed by the hotel. Nicholson looks WAY nuts right from the start. . .we don’t get that sense of him “losing it” so much as that he “lost” it long ago! Also, Shelley Duvall is so pathethic, right from the beginning, that I felt absolutely no regret when he killed her.
John Carpenter’s The Thing works way better for me than the original Thing from Another World.
I was going to say that The Three Musketeers by Richard Lester was better than the 1948 version with Gene Kelly, but upon searching the IMDB I found out that there are about ninety versions of this movie out there, and I’ve only seen three of them, so that renders my opinion suspect…
Ummm…he doesn’t, does he?
I have to agree with norinew, the TV version was closer to the book and quite good. I also agree with the statement that Nicholson didn’t quite capture the role as it should have been and that the “Wings” guy played the “slowly-going-crazy” thing pretty well.
God knows, this is not to say that the original was bad. It still ranks extremely high on my list (mostly because of those twins…yikes!) but the TV miniseries was amazingly excellent and I think deserves the nod over the original. Believe me, this goes against all my instincts to rank a made-for-TV miniseries over a Stanley Kubrik classic, but it really was darn good.
BTW, Shelley Duvall is not killed at the end of the original.
Ooops, sorry! You’re right, he doesn’t kill her. But that scene where he hacks through the door saying “heeeeeeeere’s Johnny”, I didn’t care whether or not he killed her. In fact, I cared so little, that I forgot he actually didn’t 
Mea Culpa
Stephen King couldnt direct himself out of a 2 inch hole in the ground if his life depended on it.
Well, that’s one opinion. Another is that the screen writer and/or director has a job and that is making a movie, using the book as inspiration.
If you want it like the book, read the book.
norinew maybe, like me, you wished he killed her.
I think The Lion King is a little bit better than Bambi.
The Shining and The Shining are different, but pretty equal, movies.
The first is essentially about a guy who goes nuts, the second about a guy who falls off the wagon.
[nitpick]
Pythagras, the miniseries was directed by Mick Garris, not the author.
[/nitpick]
BTW: I’ve come to expect that movie versions of King stories to be different from the printed version. Some will be missing important characters (Christine), marginally different (Kubrick’s The Shining), or totally different (The Lawnmower Man). Of course, there are exceptions (The Green Mile and a few others).