Oh, you mean like that lame-brained shot-for-shot remake of Funny Games?
Oh then you make a point. The Christopher Reeves Superman was far better than the George Reeves TV version. OTOH, Superman Returns, was dreck, although Brandon Routh did a uncanny job of channeling Christopher Reeves.
The Adam West Batman is indeed high camp, love it or hate it.
The 1954 version of A Star Is Born with Judy Garland is a remake (and in turn was remade) and is considered the best of the 3 versions. (Although all 3 versions won significant praise.)
I dispute heavily the dissing of the original Ocean’s Eleven. It is a great film, I enjoy it immensely and the remake was sludge. The walking scene at the end is one of the best shots ever put on film.
The Magnificent Seven was a quite good remake of The Seven Samurai.
Last of the Mohicans
The musical Little Shop of Horrors (1986) was a remake of a mediocre, at best, non-musical Roger Corman feature called The Little Shop of Horrors (1960), whose chief claim to fame was an early Jack Nicholson bit part as a masochistic dental patient.
I was going to suggest The Italian Job.
But I disagree with the second half of your post. I do like films from that era. I can’t say that either the 1969 or 2003 version is better than the other. They’re very different films. I will say that, while I have both on DVD, I’ve only watched the remake once and I’ve watched the original many times. But again, they’re different kinds of movies. They’re both good.
I’d call it a *homage. *
If it’s a remake then Ran is a remake of King Lear. 
I don’t think it was a great film but the John Hurt/Richard Burton remake of “1984” was better than the 1950s version with Edmond O’Brien and Michael Redgrave.
The 1922 version of “Robin Hood” with Douglas Fairbanks Sr is quite book but sometimes I think the 1938 version with Errol Flynn, Olivia DeHavilland, Basil Rathbone, Claude Rains, Trigger the Horse (deHavilland rides him), score by Korngold is the greatest film ever. Also has there ever been a father-son pair that look so much alike as did Alan Hale Sr (Little John in both) and Jr (Skipper on Gilligan’s Island)?
Richard Thomas in the 1980s did a couple TV remakes of films that may actually outdo the earlier films: “Master of Ballantrae” and “All Quiet on the Western Front”. Haven’t seen either of them in decades but that was my impression at the time.
Ken Branagh’s “Henry V” compares quite favorably with Larry Olivier’s.
Likewise, A Fistful Of Dollars is a good remake of Yojimbo.
I was searching for a precursor to the Indiana Jones series, as at least two of those films are outstanding homages to the old H. Ryder Haggard novels with Alan Quatermain. Amusingly, an attempt was made to capitalize on the Indy films with actual screenplays of the Haggard books starring Richard Chamberlain as Quatermain. The first one was a flop, which didn’t stop them from making several more.
I’d call it an homage. 
Probably the go-to answer for horror films would be Zach Snyder’s 2004 remake of George Romero’s 1978 Dawn of the Dead. A lot of us sort of expected it to suck, because the original is a classic, but Re-Dawn is almost as lauded as Pre-Dawn. Different films dealing with different issues, but I think Snyder did a good job of toning down what I always thought was Romero’s heavy-handed morality/social commentary. I love both flicks, but for completely different reasons.
I’m not sure whether this qualifies for the thread, but inasmuch as Sleepless in Seattle has the meta-connection (film-within-a-film) to An Affair to Remember, which itself is a superior remake to Love Affair, I’d say Sleepless is a damn fine remake.
I’ve never seen the original 1911 version of The Poseidon Adventure, but I think the 1972 remake with Gene Hackman is pretty good.
Whoosh?
As a recent example the remake of The Karate Kid is good. That’s not to say it is necessarily better than the original but it doesn’t pale in comparison.
I’d say Hitchcock’s second attempt at The Man Who Knew Too Much is the better one.
I can’t say if the American version of The Ring is better or worse than the Japanese original, but it is a pretty good movie on its own. The Departed was better (at least to me) than the original.
Mel Gibson’s version of Ransom is about as good as the Glenn Ford version.
I’d disagree with the comment above that Sorcerer is better than The Wages of Fear but it is still a good movie.
Ben-Hur. Not sure if i’d say it’s better, but the remake is very good.
I agree with you! I like Friedken’s version better,