Or third, fourth, etc... (I just couldn't fit it all on the subject line)
"La Grande Illusion" is the first one that comes to mind. I think part of it was watching it as such an early time (5am) and on this VHS from the library, it was not only grainy, but the subtitles almost matched the b&w movie itself. I later saw it on TCM and it's a Top 20 of mine.
"Straw Dogs" must have been too dark for me 20 years ago, and even 15 years ago, but I enjoyed it very much a couple of years ago, 8/10.
Antichrist... I actually didn't like it the first time, but then I couldn't get it out of my mind for so long, and ended up falling in love with it.
I liked The Incredibles the first time, but the second time it was so much better, and it jumped from "fun Pixar movie" to "one of the best movies I've ever seen."
Casino Royale falls into this territory, it just didn't strike me at all the first time and I ended up forgetting I'd seen it.
The old TMNT movie from 1990... I remembered it fondly after seeing it in the theater at 13 years old, but it was over 20 years later that I bought it on blu-ray and watched it again. I loved it, the movie is amazing! It was so good that I watched it yet again with my roommate like two days after I'd bought and rewatched it, and the movie didn't lose any of its impact between that second and third viewing!
Hell, it could stand to be directly remade, since human trafficking is such a big deal today. The story was pretty serious, really.
You could directly remake that old TMNT for people who were kids in 1990, and because of that, the remake could be far more serious and a bit more violent, just like the original TMNT comic was. More like an action drama, just remove the comedic elements inspired by the cartoon.
I'd also toss Krang in there, disguised as a very large-framed, heavy businessman and mob-like ruler (aka kingpin) who wears yellow sunglasses to hide his not-human-enough-looking robotic eyes. Krang himself would be hidden behind a business suit most of the time, and when he wanted to look out, he'd take the jacket and shirt off.
The funny thing is, his suit would have suspenders holding up the pants... so with the shirt and jacket off, he looks so much like the Krang we know (who has like metal suspenders, sorta).
I was so shocked to see Elias. He had basically just become a really big "name" (at least for me) in Shutter Island relatively soon before I rewatched this. If I'd seen it for my second time a few years earlier, I might not have recognized him.
Kingdom of Heaven. First time I saw the theatrical version, didn't like it. Second time I watched the director's cut, liked it a lot more. Third time I watched it (also director's cut, obviously, because who would watch the theatrical version after having seen the director's cut?), I liked it even more still. Now it's one of my favorite movies.
I'll add The Witch (2015), I found it difficult to follow with ye olde English dialogue first time round so I gave it another try with the subtitles on and I really enjoyed it.
Spirited Away. I saw it for the first time on VHS dubbed in English. I thought it was a good movie, but it didn't have the same effect on me as it did the second time, years later on DVD in Japanese with English subtitles.
Maybe I should give Spirited Away another chance, because I saw it once in the theater, and honestly kinda hated it. Just didn't feel cohesive enough, or something. I remember feeling like the story was a bit random perhaps, or a bit disposable perhaps, but I do understand that it's supposed to be more symbolic anyway.