The Body Horror of alien possession. The possession sequences usually weren't seen on-screen, but the few glimpses we get show the alien literally merging its body on top of a human.
The first-season episode "The Angel of Death" shows the aliens casually discussing their plan while a bound and gagged group of humans are trapped in a cage. The scene ends as the aliens walk over to the cage to take over several victims (including the father of a family) as they try to hop away pitifully. Later, we see the possessed father (among others) preparing to attack the team, with the rest of the family never seen again.
The cloning process Ironhorse (and others) go through in the second season. Ironhorse gets it particularly bad - kidnapped, stuck into a cloning chamber in a dark warehouse, and forced to watch as a duplicate of himself rises out and mocks him before going off to destroy the Blackwood residence.
The scene where the aliens first show their hostility - by deliberately, systematically exterminating a crowd of unarmed civilians with a heat ray and destroying every structure in front of them with their Wave Motion Gun. Human bodies turn to nothing but ash, leaving their clothes flapping in the wind. A bridge full of stopped traffic fares little better. Put yourself in Ray's place - he's running for his life, while people all around him are being incinerated. The only reason he survived that attack is Plot Armor. No mystery why he arrives home an ash-covered, shell-shocked wreck.
The Ferry scene, where we're introduced to the all-new terror of the Gatherer Tripods. Ray and family just barely survive the horrors of the sinking ferry and swim clear, only to get a front row view of the two choices humanity is given: be vaporized or be harvested. All to mingled screams of an air raid siren (from the town) and the ferry victims being gathered by the Tripods.
The marshaling call the Tripods Make. It translates from Martian to "You're fucked!" at warp speed. You hear that noise, nothing good is going to happen.
People being captured alive, both a) to feed the Tripods (which have a biological component) and b) to be used as fertilizer.
The plane crash scene is absolutely terrifying. It doesn't help that it overdoses on Hell Is That Noise.
"Are we still alive?"
Rachel stumbling across the river full of dead bodies. The look on her face says it all.
The Hobbes Was Right aspect of the crowds, like the one that threatened Tom Cruise's character and his kids just to have access to a car, and the insane mob killing each other over the car beforehand.
And then someone picks up a gun and shoots the guy who just stole the car from Ray.
The basement sequence in general, just because of how dark the mood is and how the tension slowly builds.
Rachel's facial expressions during these scenes are a bit creepy. She quite often has this emotionless look on her face, like she's seen too much to take in any more.
The scene where Ray is forced to kill Ogilvy. It's eerie listening to Rachel singing her lullaby to herself, knowing what's happening in the next room.
When Rachel wakes up to find an alien probe right in her face. Her screaming in this scene is absolutely bone-chilling.
The tripod attacking the ferry. Tom Cruise's character and his kids get treated to the lovely sight of a car that still has people in it getting flooded with water.
The Train scene. At first, while everyone is making a mass exodus, people see a train coming by. The train is on fire and a not a single noise is made while it goes right by everyone. No screams, no music; Just the sound of the train just whooshing by.Nothing Is Scarier, indeed.
Just beforehand, Rachel says, "Looks like the power's still on here." Imagine what would've happened if it wasn't and the train crossing bars didn't go down.
The total destruction of the US military forces fighting the tripods as they buy time for the civilians to escape. Imagine the Armed Forces, completely outgunned in every way and unable to effectively fight the enemy as masses of people are getting slaughtered around them. And they know it. And yet they stand their ground knowing full well they're going to be massacred just so that those around them might have some chance to live.
Not helped by the scene of flaming Humvees rolling down the hill as the tripods completely brush off the attack to resume their slaughter.