This is based on opinion. Please don't list it on a work's trope example list.
Nightmare Fuel / Independence Day
The destruction of NYC, Washington, and Los Angeles, which ends the first act. Imagine being on the ground, watching those hovering spaceships open up at the center and shoot a beam down, believing it to be a welcome message from the aliens. Then the building the ship is under disintegrates inhumanly fast, becoming a shower of debris and a wall of fire starts moving outwards in every direction, destroying everything in its path and hurling cars away. It is a fireball you can't outrun. Critics at the time praised this scene for its haunting realism, which became even more hauntingly real on 9/11 five years later. Marketing for Independence Day: Resurgence reveals this happened world wide in 33 other cities at the same time; imagine being in London, Moscow, or Paris, watching that wall of fire advance, destroying every single thing in its path. A later shot after the destruction shows an aerial view of Los Angeles after it's destroyer has fired its initial beam. There is nothing left of Downtown or the surrounding areas, and the blast wave is still moving outwards.
The ships opening is hauntingly beautiful, but serves a much more sinister purpose. The moment they start to open, everyone immediately stops to see what's happening. No one is panicking anymore and they're standing still. It's effectively like a giant bug zapper: mesmerize the primitive creatures with a bright light, then vaporize them.
It's difficult to translate the visuals to the written page, but the novelization effectively describes the devastation as "a hurricane, a flood, and an atomic bomb all rolled into one."
Not to mention the War of 1996 website shows the course of the alien invasion. Every twelve hours, the ships move to their next targets and destroy them. Then they do it again. Like clockwork.
General Grey: If you calculate the time it takes them to destroy a city and move on, we're looking at the worldwide destruction of every major city...in the next 36 hours.
President Whitmore: We're being exterminated.
Humanity's first counterattack. The Black Knights along with thousands possibly tens of thousands of pilots around the world all end up the same way, finding out their missiles are useless against the Alien shields, coming craft to craft with smaller and faster attack fighters that also have shields and being picked off one by one. Whitmore realizes he made a mistake the moment the first missile hits the shield.
Crewman: Squadron Leader! Do you read?! Abort mission!
President Whitmore: This isn't happening fast enough. GET THEM OUT OF THERE!
"Reports indicate that this battle has repeated itself all over the world with the exact same results."
At the same time that the Americans were engaging the New York, Washington, and Los Angeles destroyers, the rest of the world was doing the same. The RAF was engaging the London destroyer, the Luftwaffe was assaulting the Berlin destroyer, the Japanese Air Self-Defense Force was getting revenge for Tokyo, the Royal Canadian Air Force was fighting the Toronto destroyer, the Israeli Defense Forces were avenging Jerusalem, the People's Liberation Army Air Force was fighting over the ruins of Beijing, the Iranian Air Force was fighting over Tehran, the list goes on from Mexico City to Seoul. Not one counterattack was victorious.
Following that, the alien communicating via Dr. Okun and making the aliens' motives horribly clear:
President Whitmore: I know there is much we can learn from each other, if we can negotiate a truce. We can find a way to coexist. Can there be a peace between us?
Alien: Peace? No peeeeace.
President Whitmore: What is it you want us to do?
Alien: Die... dieeeeee...
Some meta-context is needed to explain why this was so frightening. While films with aliens killing humans were quite common even before this film, most of these were slavering B-movie monsters, or otherwise incapable of communicating with us. Aliens that could talk to us were usually friendly. The aliens in this movie are among the first notable aliens shown to be able to communicate with us meaningfully for the sole purpose of telling us they're gonna kill us.
Then the alien uses a psychic link on Whitmore to show him about its species. The novelization goes into more detail, but it's Fridge Horror at best on what he saw: countless battles across countless worlds, many species slaughtered, whole civilizations scorched, the invaders land and establish their own settlements, then they consume the planet's resources until there's nothing left and go back to the mothership for their next journey.
The point inside the mothership where Hiller and Levinson fly over a staging ground with thousands, if not millions, of alien soldiers assembled, waiting to board transport ships. Hiller speculates that they're likely a ground invasion to wipe out any last vestiges of resistance on Earth, and given the numbers of the invaders, it really drives home the point of what will happen if they fail their mission.
The novelization goes into a lot more detail about nightmarish elements:
Russell has a flashback to his abduction. One night, he's out working on an airplane engine in a hangar. Then suddenly his body is paralyzed. He obviously thinks it's a stroke, but then he begins hearing the aliens say "You will not be harmed." Then they break out the probes, all while Russell is looking out a viewport at Earth from the lower atmosphere...
We also are treated to a flashback of the Roswell crash. Even though the aliens are utter assholes, their crash is still terrifying to read. Their carrier ship jumps away, as they were on the verge of being discovered, and because of that, their power systems quickly died. One of the pilots was killed in the crash, and another tried to crawl away from the site, but was attacked by coyotes.
The post-war world. The invaders have been resoundingly defeated, but the damage has been done. Imagine 1945 Europe on a global scale. 108 cities, from New York to Shanghai, Berlin to Moscow, Riyadh to Pyongyang have been obliterated. Nations and their militaries are in ruins. Millions, likely billions, are dead and millions more are now displaced. The cost of rebuilding and the sheer scale of restoring what has been lost is incalculable. Factor in how long it took to rebuild Ground Zero after 9/11, then scale that up to all of New York and multiply it by 108. Needless to say, it will likely take decades before every city is rebuilt and trillions upon trillions of dollars.
The alien city ships are pretty terrifying. There's no beauty to them; they're giant work barges built to do one job. They just hang over cities ominously with no broadcast of their intentions. Then they open, bathing the city below in greenish light, fire their weapon and utterly annihilate the city, close, and move on their next target.
The ungodly horrible noises the City Destroyers make when they enter our cities. When NYC gets shadowed by the ship, the engines give out a horrible loud moan. The moment the ship exits from the fireball it gives out the most stomach churning noise ever given off from a spacecraft in film. It sounds like something you'll hear in a HP Lovecraft story.
The giant fireballs in the sky that form from the ships entering Earth's atmosphere. "Harbingers of doom" describes them perfectly.
Speaking of the fireballs, the AWACS scene. They're trying to identify the disturbance off of California with zero visibility. They reach a clearing...and suddenly the sky is entirely on fire. They try to pull up, but get engulfed...
Not to mention the attackers. Those nimble little things just dart of their parent ship like hornets and proceed to annilate their assailants. They can also easily move at speeds that are the limits for human aircraft.
When we finally get a full view of it, the mothership is extremely unsettling. It's over 500km in diameter, tar-black with no external lights, and looks as though a moon had been sawed in half and given fangs.
The scene where Hiller goes to pick up the paper. There's very little music as he slowly looks around him, seeing all the neighbors are packing to flee the city. Then he looks up, sees a helicopter flying overhead...and then a massive ship hovering over downtown Los Angeles. In addition, this is the first shot that both shows a majority of the ship and gives something appropriate to give its scale. The ship is so wide, it can't entirely fit within the frame. The entire Los Angeles basin is dwarfed by the behemoth, compared to an ant hill underneath a car.
The aftermath of the first wave. As July 3 opens, we see the New York City Destroyer still hovering over the smoking ruins of the Big Apple. The Statue of Liberty is half submerged, the tops of both World Trade Center buildings are sheared off and the interiors are burning; there's no sign of any living human within twenty miles of ground zero (the Empire State Building). All of Battery Park is in flames and most of the skyscrapers that once defined the Manhattan skyline are nothing more than burning, skeletal remains. Then, as silently as it opened, the City Destroyer closes its main cannon; it's getting ready to move to its next target of Philadelphia, just like the 35 other City Destroyers throughout the world.
A lot of the fake news broadcasts, which can be found on the 20th Anniversary bluray, show a darker side of first contact. For instance, there's one segment that mentions the UN effectively dispanding due to disagreement about how to proceed with meeting the aliens.