Defeating Gnasty Gnorc in the first game will feel this way to most players in their first playthrough.
The first time you successfully ace a speedway may also count.
The fight against Ripto in "Gateway to Glimmer" (name may vary depending on your location), in which you both fight for MacGuffin powerups and proceed to fight it out on a platform, at which point he will create robitic versions of Gulp. Then after that Ripto will sink the platform you're fighting on and jump on a cyborg bird- you promptly get a powerup and give chase, dog-fighting all the way. To say nothing of the mini-games that follow.
Each boss battle in Year of the Dragon is amazing, but both ones against the Sorceress are absolutely fantastic.
The mini-games:
The skateparks are all pretty cool, and getting the course record feels damn cool.
Hunter's manta-ray from the second game returns, and you go around hunting the metallic sharks that also returned. Laser-Guided Karma at its absolute finest.
There is one where you can play as Sgt. Bird and fly around Enchanted Towers, giving a Curb-Stomp Battle to any enemies in your way, while completing the regular quests. (This option will likely be available after you've completed the level the first time round, though.
Super Bonus Round from Year of the Dragon. Full stop.
Sheila, Sgt. Byrd, Bentley and Agent 9 get one each upon being released by teaching Moneybags a lesson in their own unique way; kick, rocket launcher, club and laser gun respectively.
At the end of the third game, you get to chase down Moneybags and burn him until he drops all of the loot he took from you throughout the game; then force him to give up the dragon egg.
Butler saving The Professor at the end of Spyro: Attack of the Rhynocs.
The Legend of Spyro trilogy
The final battle of each game gets one:
A New Beginning: Spyro uses his full power to blast Cynder so hard he knocks her out of the Dark Master's control
The Eternal Night: Spyro is exposed to Malefor's evil power, turning him into Dark Spyro. Dark Spyro then proceeds to turn Gaul to stone and shatter him to pieces.
Let's not forget when Spyro flips out after Ignitus's apparent death in the Burned Lands only to have Cynder snap him out of it with a calm "Don't do this."
Dawn of the Dragon: The entire Final Battle is one long one. Spyro and Cynder fight the Big Bad first in a dog fight, then while falling down a volcano to the center of the planet where they finally defeat him in a Beam-O-War.
Also, Ignitus gets one in the first game when he shows just what a fully trained dragon can really do to a bunch of apes. Another group of them end up suffering this in the second game in another such moment during the Ape raid on the temple.
Sparx finally snapping and punching out Sniff in the Sky Pirates arc of the second game.
