Groudon and Kyogre's epicbattle in Pokémon Emerald. And more importantly, Rayquaza, who flies to Sootopolis after you encounter it at the Sky Pillar. Once you arrive there and witness Groudon and Kyogre again, Rayquaza comes out, flies through the clouds, descends with a trail of green light cloaking it, and swoops down to Groudon and Kyogre. With one mighty roar, it sends them both away, and departs, returning the weather to normal. How intense is that?
Take note of Groudon's situation in particular in this fight: it's completely surrounded by water, the weather is predominantly raining throughout the combat, and it's weak to water-type attacks, yet it still manages to fight on even footing with Kyogre.
Earning the Gold Shield ornament after winning 100 straight battles in the Battle Tower definitely qualifies as one for the player and his/her Pokémon.
Or managing to get the gold symbols in the Battle Frontier, especially with all the crap they put you through.
For Red/Blue veterans of Mt.Moon, the ability Soundproof, which negates all sound-based moves, feels like all Christmasses come at once.
WILD ZUBAT used SUPERSONIC! WHISMUR's SOUNDPROOF blocked SUPERSONIC! [victory lap]
Riding on a dragon and saving the world from a giant meteor? What more could a 10-year-old dream of!
Omega Ruby and Alpha Sapphire
In the original games, Groudon and Kyogre's special abilities automatically summoned permanent sun or rain to the battlefield. Unfortunately, a Nerf in Gen VI changed the abilities to just an automatic Sunny Day or Rain Dance, ending their effects after five turns. Then comes Omega Ruby and Alpha Sapphire, and the introduction of Groudon and Kyogre's Primal forms, who have two new abilities: Desolate Land and Primordial Sea which, besides sounding really badass, came with a few new effects:
Made the sun/rain permanent again as long as Primal Groudon or Primal Kyogre are present.
Once one of the abilities is activated, the weather cannot be changed by a normal Rain Dance or Sunny Day.
It gets better. Mega Rayquaza's ability, Delta Stream, lessens its weaknesses as Delta Stream negates any super-effectiveness against Flying-types, thus taking its 4x weakness against Ice to only 2x and negating its Rock weakness altogether, making it much less easily taken out by Groudon or Kyogre. Which makes sense.
Mega Latias and Mega Latios can be ridden as mounts, allowing you to fly across nearly all of Hoenn, including to the mysterious clouds shown in the region's official art and the various small islands dotted around the region. For what purpose, exactly? To find every non-event legendary Pokémon that wasn't in the original Ruby and Sapphire or X and Y.
In a meta-moment, for all the flack people gave Generation III, the lines in Japan finally put the case to rest: the fanbase loves Hoenn. These are just lines for pre-orders and they span from Sendai, Nagoya, Sapporo, Yokohama, Fukuoka, and Tokyo Bay. Let the trumpets sound.
Wally's already badass by time you make it to Victory Road, but the remake highlights his major improvement; you fight him in a field of flowers at the end of Victory Road, he gets a slightly tweaked introduction for the fight and the Music is redone from the generic trainer battle music that was in the original fight.
Starting with Lavaridge Gym, his name will always be on the gym statue before you even get there. Meaning he keeps beating the gyms before you do like Blue! Pretty awesome considering the last gym you saw him, he only had one level 17 Ralts. Even if excusing it on the player getting distracted by Aqua or Magma, the feat is still amazing.
Further reinforced in a blink-and-you'll-miss-it moment during the cut aways to different areas of Hoenn after you catch/defeat the respective legendary, where you see Wally at Ever Grande City, possibly about to enter Victory Road.
During Episode Delta, his keystone gets stolen. His initial response isn't to break down but adamantly states his priority is to protect his family, lack of Mega Evolution be damned.
His post-game team (after you beat a Chatellaine on a Super line) then takes it further. His team levels range from high seventies, with Gallade at 81. Furthermore, a large portion of them use sets actual competitors use. Wally could essentially pick a fight with the likes of Steven, Cynthia, or Red.
The newly-revealed Delta Episode, which apparently involves riding Rayquaza into space to fight off an asteroid, which is also Deoxys - and from the details revealed, there are links to the war in Kalos from 3,000 years ago. This is awesome for three reasons:
Firstly, just re-read that description. Riding Mega Rayquaza into SPACE!
Thirdly, just how unexpected Deoxys' appearance is.. All you know is that a meteor is on a crash course towards the planet and there's a dragon-user going around trying to harness Rayquaza's power to prevent it. Then you catch Rayquaza yourself after it deems you worthy of facing him and not Zinnia and after defeating Zinnia you ride Mega Rayquaza into space and it pierces through the meteor. Threat cleared! But then you see that lone triangular object floating among the chunks moving in triangular patterns until it grows red and tentacles emerge behind it, with Deoxys' theme kicking in as very familar tentacles emerge from the object until it breaks and reveals the DNA Pokemon, finally obtainable outside of events and spin-offs, who then lunges at you, kickstarting the epic battle against a legend 10 levels higher than your newly adquired Rayquaza. No hints were ever given that Deoxys would ever appear, and that it was never catcheable in-game unless you got lucky with events only adds to the unexpected of the moment.
The receptionist of the Weather Institute. She notes that there is some "disturbance" on the second floor (i.e. a hostile takeover by Team Aqua/Magma), and then says she's not even rattled, since she's a professional. Not bad for an NPC.
Previously in Contests, if you filled the audience's excitement meter, you'd simply get a large point bonus and be told that the crowd is really excited. Now? Your Pokémon does a Limit Break style move, some of which look really badass. And if your Pokémon can Mega Evolve, it gets even better.
The buildup to the battle with the version legendary. Like the originals, the battle is within the Cave of Origin, however, when you get to the place where you fought the cover legendary originally, you have to ride the version legendary's back with the help of a suit created by the version's villain team and the orb of the opposing version. Then, when you get to the deepest part of the cave- where the energy for Primal Reversion is- you jump off and watch as the legendary undergoes Primal Reversion and towers over you as it challenges you. The cutscene of the transformation alone is amazing.
If that wasn't incredible enough, the music probably alone makes it a Crowning Moment of Awesome. The music even starts before the battle begins. During the transformation, you hear an energetic rock/orchestra remix of the Groudon/Kyogre battle from the original. Not only is it not just a simple updated version of the original track, the extra instruments truly convey the awesomeness of facing against a mighty beast from thousands of years ago, let alone one that pretty much nearly ended the world via floods/droughts, and isn't hesitant to do it again. After the transformation, the Primal-reverted Pokémon challenges you to a battle, to which the cutscene seamlessly goes into, with the music still playing.
What's even more awesome, is that parts of the song have the GBA MIDI track from the original Ruby and Sapphire running in the background. For those familiar with the original, it's a hell of a nostalgic treat, as well as an amazing callback to the originals.
All of that going on while you, the player, are fighting to save the world by taming the beast responsible for threatening the existence of every living thing in Hoenn. This is truly one of the greatest epic moments the series has to offer.
For reference, the Uber Tier wasn't even entirely real until then. It was basically "anything goes" given a name, for things that were too powerful for other tiers. Mega Rayquaza basically broke the Smogon tiers and topped that.
The credits are really cool as well as a Crowning Moment of Heartwarming, showing you not only moments throughout your adventure but also what Pokémon you were using at that time, even during some more obscure moments. Then after the credits you and May/Brendan arrive at the pond where you first battled and they challenge you to one final battle, this time showing that they finally were able to obtain a Mega Evolution.
Zinnia destroying the device for transporting the meteor to another dimension, saving the Pokémon world of the first five generations from a fate it could not have prevented.