The PS4 trailer shows a Frost, Nyx, and Ash rescuing a newly awakened Excalibur in an excessively awesome (and entirely possible in-game) display. The high point is Frost freezing Captain Vor leading the capture attempt with a massive ice blast and stepping aside, allowing the Excalibur to slide in and chop him in two with a spin attack.
The gameplay trailer where the first three Warframes and Rhino slaughter their way through a Grineer army.
The first time you do a charged melee attack on a poor Grineer. It really sets the tone for the game.
The first time you slide on your knees down a ramp while blowing away multiple enemies. Yeah, it's one of those kinds of games.
The first time you manage to defeat a Stalker on your own and/or get a blueprint of one of his weapons.
This one has been made extremely difficult, as the Stalker is able to deal incredibly high damage and dispel or ignore all ability effects that don't cause direct damage. Rhino's Iron Skin and Loki's and Ash's invisibility won't save you anymore.
The first time you defeat any of the enemies that come after you like the Harvester or the G3 is also this.
The 'Operation Slingstone'' event, that tasked the players with destroying massive Grineer warships, was the first one that could actually be lost. The developers later admitted that they expected the players not to completely succeed in it. Instead however the community managed to beat it completely.
The Gradivus Dilemma event. It was an unprecedented event where player actions would actually decide which faction would control Mars, tied into in-character roleplaying posts by Alad V and Sargas Ruk, with the result that the event had record participation from players, along with the greatest sense of player participation and enthusiasm.
Credit should also be given to the players supporting the Grineer. A player hacked four conflict nodes, setting those nodes to Corpus victories; as a result, DE removed those nodes from the event victory tally. The Grineer players still managed to achieve victory even after losing four nodes.
The Grineer supporters were apparently so determined that they messed up developer plans for the event, forcing them to make changes mid-way through, three times.
The best part? There is no Gameplay and Story Segregation. Every single action and ability seen in the trailer can be executed in game. Even Rhino going fisticuffs can be done provided you have one of the gauntlet style weapons (Rhino in the trailer moves exactly as if he had the Obex gauntlets mounted, although they're not shown in the video).
The powers on display work as advertised (eg. Volt's shock can and will take out large groups of MOAs).
The one unreplicatable in-game bit is still incredibly awesome. Rhino pounces on the downed Zanuka, then starts beating on it, then grabs it and rips it in half.
Part of that is actually able to be replicated in-game. Granted, you can't rip enemies in half, but the whole "stand over a fallen enemy and beat them savagely with your fists" thing? Totally doable in-game. And yes, this sometimes results in the enemy getting split in half. Lengthwise.
The faction conflict missions where you can pick sides. Not only are you mowing down the opposing force, leading the charge of the allied soldiers - you're also moving between two warring ships in some missions. When working for Corpus you are propelled/teleported right into a Grineer frigate. Grineer however aren't as subtle and just ram their ships into the Corpus ones to make tunnels. Seeing the grand scope of two groups fighting against each other really gives you idea of the conflict.
One of the moves of the new Wolverine Claws style Venka blades involves headbutting your enemy to death.
The revamped Tutorial in its entirety. Instead of having to be saved by other Tenno, you manage to escape Vor's outpost singlehandedly, cutting through scores of Grineer and even having a short standoff with Vor himself. All while intense music plays in the background.
Vor himself has Took a Level in Badass. In the original prologue, he doesn't appear until the end of the segment, but this time, he personally leads the Grineer in awakening the Tenno, and successfully subdues you by dropkicking you to your knees and injecting you with a Mind Control parasite. Only the Lotus' timely intervention saves you.
The death of the original Mirage. Alone vs a Sentient army, she runs out of energy, has a ship dropped on her, loses her shields and her weapons. Does she give up? No, she starts tearing them apart barehanded while laughing like a loon. And she is a caster.