I agree with you about The Killing Fields.  Too often a "statement" film gets treacly and overly preachy.  This one navigated some dangerous waters very well.

My tastes run to all corners, but following is a list, although not comprehensive, of films that I think got it right in all areas.

Vertigo - I could add several other Hitchcock films to this list, but this one has always stood out to me.  The stylization fits the story, and Jimmy Stewart's performance was so subtle that for a long time after first seeing this I couldn't watch one of his comedies without looking for the neuroses....

Touch of Evil - Orson Welles exceeds the standard he set earlier with Citizen Kane and The Magnificent Ambersons.  Every young filmmaker tries to emulate the tracking shot at the beginning, and Welles only gets better from there.

Godfather Pt.1 -The very first theatrical cut - Coppola nailed it.  Downhill from there, although part 2 has some better moments, part 1 is the better overall film IMHO.

American Graffiti - George Lucas proved he could tell a story with this one, and the music and settings provide a perfect sense of time and place, right before the world went and got all nutty.

Young Frankenstein - To me, the epitome of Mel Brooks.  Derivative, childish, and overacted.  But done perfectly in every way, and it stands up over time much better than some of his other work.

Wings of Desire - The English/German original remade as City of Angels.  Wim Wenders packs each shot with gravity and sincerity, and I've never before or since seen anything where Peter Falk could move me.  I put this one on every November.  It reminds me of what can be right with the world, which overrides the cynicism that the holidays bring.

Leaving Las Vegas - This film has its detractors to be sure, but it told it's story so well, and I'm a real sucker for Las Vegas, Elisabeth Shue, and Mike Figgis films.  Check out Stormy Monday if you're ever at a loss for something to see.  Interesting performances from Tommy Lee Jones, Sean Bean, and Stink.

Gangs of New York - I could put 2 or 3 other Scorsese flicks on here, but this one has stayed with me.  The fact that it took him decades to finally get this story on film may have something to do with it.

Rashomon - I had to pick one Kurosawa film, and this is it.  The images, the sound, the acting.  I don't think Hollywood has ever done as well.

The Fisher King - It may not hold up that well in another 10 years, but this is another one that I feel like I have to watch every year or so, just to maintain what humanity I have left.