Oblivion. Brief shot of Statue of Liberty’s ruined arm. Your turn.
Planet of the Apes
Cloverfield.
Deep Impact.
A.I.
Independence Day
Deep Impact
It was far from destroyed, and actually in impossibly good shape considering how thin the copper skin really is compared to the hardened concrete buildings that are apparently gone without a trace.
I don’t recall whether the Statue of Liberty appeared in Escape from New York, but she sure took a beating in the movie poster.
Gotham has its own Statue of Liberty in Batman Forever, at least until Two Face’s helicopter gives it a face-lift by crashing into it.
Yeah, Liberty Island is an HQ for the prison in the film, so she’s fine. 
Don’t recall if it was “ruined”, but in the (first) “X-Men”, it at least got a bunch of holes poked into it. And I think it got a little chewed up when Magneto’s machine blows up.
Debatable: “Ghostbusters 2” (“she” was walking and moving, yet there were never any hinges or joints designed for this - at least “ruined” in my book)
In the original script for The Watchmen, it was a botched hostage rescue at the Statue of Liberty (which resulted in its destruction) that led to the government crackdown on masked vigilantes.
Day After Tomorrow. Hit by giant tsunami.
Well… assuming the whole movies takes place in what is now southeastern New York which has undergone significant climate change to the point where the mainland extends to what is now Liberty Island (and it must be more than just the recessing of the Atlantic Ocean, since the statue is partly buried)…
…I kinda lost my train of thought, there. If you were close enough to the Statue of Liberty to identify it as such, could you not see the buildings of Manhattan, or their remains?
In Children Of Men they show it being destroyed in an ad by a nuclear terrorist attack
The Statue of Liberty gets it in the comic books, too: Kamandi #1
Spaceballs
Really? I don’t remember that at all …
Yes, but don’t forget, he’d been finding evidence of a vanished Human civilisation throughout the movie. It’s just that he didn’t know where he was until he found that one specific structure he recognised.
The first sequel actually does show a lot of ruined skyscrapers around the statue.
The torch gets bent in “European Vacation”
It had a big hole in it in Judge Dredd.