The opening of Fargo, in which a car emerges from a dead-white screen.
The opening scene of The Holy Mountain where the alchemist spiritual leader character initiates the nude women is an opening scene that strikes me as among the best.
Orson Welles’ Touch of Evil also came to mind immediately after reading the thread title, but Touch of Evil has been mentioned upper thread.
They did in the director’s cut. Only watch that a version.
In terms of opening shots, I can’t believe nobody’s mentioned* Eyes Wide Shut* yet! (It’s last shot/line ain’t bad either…) 
Slightly NSFW: Eyes Wide Shut - YouTube
Gladiator, though, technically, the first 30 seconds or so are kind of boring
https://www.youtube.com/watch?v=0ZghMKa4jGo
Memento, which starts with a Polaroid photo of a murder scene that gradually fades. Then the photo goes back into the camera and we see the murder take place backwards.
Aaah, thank you! Since I’m beaten to these, I’d go for Aguirre. In the audiocommentary, Werner Herzog mentions that the clouds broke up at just the right moment to shoot the breathtaking procession of people, poultry and pigs down that tiny goat’s path, how glad he was about having been able to persuade Kinski not to have the ruins of Machu Picchu (and lots of close-ups of himself, of course) in it and that he felt blessed when even the sun came out…after listening to the rest of it, I couldn’t help but wonder if some ancient deity wasn’t having a quiet chuckle after these gracious gifts. 
I’ve waxed about it before, but the opening scene for Mario Bava’s Black Sunday is an atmospheric masterpiece of light and shadow, as is the rest of one of the most gorgeous pieces of gothic horror I’ve ever laid my eyes upon.
Certainly not THE best, but after the first iconic minutes of Faster, Pussycat! Kill! Kill! you just know that you’re in for some wonderful pulpy fun. Ladies and gentlemen, welcome to violence!
Serenity, a great movie from beginning to end.
It begins with what seems like the opening exposition that a thousand other science fiction movies have before their opening credits. Then you realize that it’s not general movie exposition, it’s a teacher talking to her young students. Then you realize that it’s not actually a classroom, it’s a dream in River’s head while she’s being studied by Alliance scientists as if she were a lab rat. Then you realize that the lab is not being shown in real time, it’s holographic security footage being watched by the Parliament operative. Then there’s a fantastic scene as the operative deals rather severely with the lab personnel who let River escape.
And then the opening credits start.
Some not mentioned :
Reservoir Dogs
Highlander
Pitch Black
I enjoyed the opening of “Casino Royale”; it did a great job of introducing the new Bond without an outlandish and unrealistic stunt. And the title sequence didn’t have a bunch of beautiful nude women in sillhouette!
The Rundown - The Rock walks into a crowded club and beats up 5 football players, taking out the last guy by chucking a turntable at him from across the dance floor. The rest of the movie is meh, but that scene is awesome.
I’ve always liked the opening to Apocalypse Now with the jungle, This Is The End, the napalm going off, the helicopter noise morphing into the sound of the ceiling fan, the Captain doing his dance or whatever and winding up getting all bloody… great mood-setter.
Fantastic scene, but it’s not the opening. The opening is the salesmen and office manager meeting before work in a bar.
Uneven as the rest of the movie is, the opening credits of Watchmen do a great job of setting up the world.
I agree with The Lion King. The Circle of Life sequence is easily one of, if not THE, greatest animated sequence Disney has ever created.
The Dark Knight - no opening credits, no exposition, just straight into Joker’s bank heist.
Spaceballs did it even better! The cruiser just kept going and going for like 2 minutes! I was laughing my ass off before a single word was spoken!
Which would lead to “great closing lines/scenes” were it not a hijack. (I can’t think of a better ending for the movie/series. At all. Destruction. Renewal. Soaring symphonic score. And… “What was that?”)
The first scene in The Ring is really effective. It’s very much like your typical, cheesy teen horror flick - and yet it’s not. Two teenage girls home alone on a rainy night, spooking each other out with scary stories and pranks. If you don’t know anything about the movie, as I didn’t when I saw it, you really do think it’s going to be the usual schlockfest. Then the tension starts to get authentic and the last twenty seconds or so really pull you in and set the mystery in motion.
Another good one in the horror genre is It Follows. A young woman comes out of her house half dressed. Shot from the camera’s pov (is that the right term?) we follow her as she runs in a frenzy around the street. We have no idea what she’s freaking out about, it daylight and there are other people on the street who apparently can’t see what she’s seeing. Then we cut to the next day and see the aftermath. Yikes.
The opening scene / sequence of the movie Up certainly qualifies. It had lots of people in tears to see the progression of the loving couple losing a baby and then the wife as the man drifts into old age alone.
On a happier note, how about the hills are alive with The Sound of Music.
An oldie that I still enjoy now and then: Sharky’s Machine Opening