Loved by critics, not so much by the public, or dissed by critics, but embraced by the masses. What films are examples of this dichotomy?
The first that popped into my head was The Blues Brothers. Critics were meh to hostile as I remember. But I’ve never met anyone who didn’t like it.
Two that come to mind are Predator (1987) and Psycho (1960 )
Both had mixed reviews when they were originally released, however the outstanding public support caused many critics to eventually re-review the movies and in their own ways are considered classics nowadays.
Not 100% if they both were popular, but Stanley Kubrick’s Dr. Strangelove and 2001 a Space Odyssey are notorious IMHO, as it was really embarrassing to see that many critics originally panned the movies and nowadays when you check Rotten Tomatoes the movies are close to 100% fresh in the tomatometer.
Makes you wonder how many critics hit the reset button, and I also guess that most of those original negative critics are pushing up the daisies nowadays.
Going by memory, the first movie that comes to mind is Ace Ventura: Pet Detective. I don’t think that movie got a single positive review and most were outrightly hostile. Despite this, the film was a huge success and launched Jim Carrey to movie superstardom.
I could have sworn that Roger Ebert had put out an entire book of his own reviews that he had come to strongly disagree with. I thought it was titled something like “I Was Wrong”. I can find absolutely no evidence that any such book ever existed.
I don’t know how I conjured such a specific memory of actually holding the book in my hands and paging through it in a Barnes and Noble. Perhaps he had a section in one of his books featuring reviews that he later came to disagree with.
Any one of the Dean Martin and Jerry Lewis movies.
Friday the 13th
Independence Day
critics just didn’t appreciate what it was trying to do man
The first “dissed by critics, loved by the masses” films that come to mind are Highlander (the original), Office Space, and Army of Darkness.
A wise man once said: “Do or do not, there is no try”. 
The critics were right.
Tom Laughlin was so chagrined by this phenomenon in regard to his “Billy Jack” films that he actually suggested approaching “our” legislators to see to it that all movies got a favorable review along with a pan. Poor sucker’s still trying to foist his ideal of utopia off on the rest of us, but his fan base has largely deserted him for different delusions…
The Hurt Locker. Loved by critics. Not very commercially successful until after it won the Oscar.
Nearly all poorly-rated movies by Time made money and many became top-grossers. That’s how I remembered things during my “Time Magazine” years.
I’m not sure it fits but Blade Runner was originally panned by critics and flopped badly at the box office, but eventually became a huge cult hit and is now regarded as a classic.
Ironically enough, had it been made even one or two years earlier, prior to the VCR explosion, most people reading this would never have heard of it.
The Shawshank Redemption was originally beloved by critics, but flopped badly at the box office, but eventually became a huge hit.
Titanic was panned by critics, but… well… I don’t think I need to tell anyone just how well it did in the box office.
Hmmm, I can picture the same thing. (Unless I am thinking of his book “I Hated, Hated, Hated This Movie.”)
No it wasn’t. It got mostly favorable reviews. Rotten Tomatoes has it at 87%.
Citizen Kane? I would guess high critical acclaim and low popular opinion (during its time).
Titanic was not panned by the critics at all, it won 11 Oscars, several Golden Globes and was near universally thought of as a great movie by critics. Titanic suffered a backlash because of it’s popularity, it became fashionable to dislike it. I remember watching it again a couple of years ago and being surprised that it actually was a good movie. But, DiCaprio and Winslet are excellent actors, as they have proved time and again this last decade and a half. And, Kathy Bates, Billy Zane, Victor are not bad either.
I imagine Adam Sandler’s oeuvre would qualify, for the most part.
A lot of the movies named so far were ones which were disliked by both critics and moviegoers when they came out but which have since been rediscovered by both critics and moviegoers. That’s not really what the OP is asking for, I think. Some of the ones mentioned were actually liked by both critics and moviegoers (at least by those who got to see them) when they came out but didn’t get marketed well by their distributors. They have become more popular since then, but the original failure to sell well was the fault of the distributors, not the critics. A clearer example of what the OP is talking about is Transformers: Revenge of the Fallen:
This film was really loved by audiences but mostly hated by critics.