Barry's abduction scene, the general scenes of electronics going haywire, and to many, Roy's obvious descent into alien-induced madness. It's just so very deadpan and the setting so banal, yet his madness is profound.
Jillian's attempt to phone for help being frustrated by the aliens having tapped into her land line. The repeating five tones create the effect of a Madness Mantra while also driving home just how helpless and alone Jillian really is.
Johnny Mathis singing "Chances Are" is just the cherry on the icing.
According to the making-of documentary, Barry's actor wasn't afraid of the abduction scene at the time. Not only was he 'abducted' into his real-life mother's arms, but Spielberg had told him all about what was going to happen a few hours before. This adds to the scene - imagine your child is being taken from you by force, and he wants to go with the kidnapper.
"He says the Sun came out last night. He says it sang to him." (YMMV on whether this is terrifying or like a description of a beautiful religious experience.)
The scene where the government gases the escapees trying to climb Devil's Tower is very disturbing.
And approaches Fridge Horror when you consider that the order to deploy the gas was issued with no cautionary warning to avoid dosing the trio with it when the climbers were, say, halfway up a high, sheer cliff.
The scene where Roy is in his truck and has an alien encounter - especially when there's a bait and switch when you think the truck's lights are a UFO (and then the UFO's lights resemble a truck's!)
The unnerving way the aliens bring back objects like the planes flown in Flight 19... but not the people until the end. And leaving them in places where those planes and ships do not belong.
The India sequence where the mass of people are chanting the alien message over and over is eerie enough. But then everything quiets down as we hear a lone voice asking (without English subtitles) where the music came from and suddenly everyone shouts and points skywards - a thoroughly startling moment for those not expecting it (especially in the theater).
Although this is no longer the case to modern-day viewers used to seeing worse, and Spielberg tried his best to make the aliens look and act benevolent, but considering the "Grey" type of alien had rarely been seen on screen before, the first-ever glimpse of the aliens to 1977 viewers was unnerving, especially the tall and skinny alien seen first.note She's often described as "the spider alien" because she comes out on all fours at first, as if Spielberg wanted us to think "whoa, are they giant spiders?" for a second. The only film with a "Grey" alien was 1956's Earth Vs. The Flying Saucers and on TV there had been a couple episodes of The Outer Limits (1963). They certainly were familiar to science fiction fans and readers of speculative UFO literature: Betty and Barney Hill, two of the most famous abductees, described aliens who looked like this. But they would have been largely if not completely unfamiliar to the average viewer at this time. They have somewhat of an "unfinished" look to them; as though someone started making a human and then stopped once they though enough had been made to get the point across.
from Sesame Street may unintentionally give you the creeps now, thanks to Soundtrack Dissonance.