The two prime examples I can think of are Bryan Singer's X-Men movies:
And Super Mario Bros. The Movie:
(stay with me...)
Now, that doesn't mean I don't love a good 100% faithful adaptation -- I do! Sin City, 300, the (first two) Spider-Man movies, even the recent Marvel-produced movies are largely, with only slight exceptions (or in some cases, none at all), committing the comics page to screen, and I love that!
But, I also love the idea of breaking things down to what they are at their core.
For example, my favorite of the Punisher movies (relative to each other) is the first one, because it felt like what the Punisher would really be like in the real world. He's not a dude in black spandex and a skull logo spouting poetic verse about how the guilty must be punished, he's a dirty, greasy, disturbed, dead-eyed headcase who lives in the sewers and only comes up to murder criminals.
(while spouting poetic verse about how the guilty must be punished)
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(technically, my favorite Punisher movie is Man on Fire...)
(...but that's neither here nor there.)
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"What would the X-Men be like if they existed in the real world?"
Well, they wouldn't be brightly colored superheroes beating up supervillains, they'd be a paramilitary force dressed for combat, fighting a secret war against a ragtag group of terrorists.
Because, here's the thing... when I look at a comic -- and primarily, I'm talking about superhero comics here -- I'm seeing the real world cast through a fantastical lens. And I enjoy it! It stimulates the imagination to contrast these things against what I know to be true.
So, conversely, taking the fantastical and casting it through a realistic lens has much the same effect. It's taking one thing and shaping it into a different kind of thing, while still keeping what made the original thing distinctive.
And it's the same for Super Mario Bros!
"What would Super Mario Bros. be like if it existed in the real world?"
(and I love this part)
"It would be FUCKING BLADE RUNNER!!!"
Of course it would!
Seriously, what an act of sheer invention. To take this nonsensical world of castles and mushrooms and evil dragon/turtle/monster kings and heroic plumbers, and turn it into a gritty cyberpunk dystopia where the meteorite that supposedly killed the dinosaurs actually split the Earth into two parallel dimensions and oh fuck it, just let the movie explain.
I can honestly say that a 100% faithful adaptation of the game to live action would not have been anywhere near as interesting as the film that was made. Yet it still had all the little elements that made it distinctly Mario Bros. They were representations and approximations, but they were there. It felt like this crazy little Elseworlds version of the video game.
And that's really the point, I guess. Movies can be that, because they'll never be the original thing. And sometimes it's better to invent (or reinvent) rather than adapt, because ultimately, all the latter means is that you're being told a story you already know -- and the first telling is usually better.
Movies that aren't afraid to change things up may very well end up crap...
(cough)
...or they may end up showing you your favorite thing from a new angle.
And as long as it's still about a group of outcasts protecting a world that hates and fears them...
...or a couple of stalwart plumbers saving the princess from a tyrannical king...
...then it still maintains what's special about the original.
And despite what many may convince themselves of when trying to win arguments on the internet, that's really all that matters.
After all, I can think of another series that follows this pattern...