Here's mine. Just a random thought in my head. Gaming moments either from cutscene/gameplay that really draw you into the game and leave you breathless. 

5. Fallout 3: Walking out of the vault for the 1st time - never played much much of any Bethesda games until Skyrim; but I was 14 at a friend's house watching when you first step out of the vault into the huge open world. Awesome stuff. 

4. Prince of Persia (2008): The visual style - if you haven't played 2008's PoP game you need to. It had a beautiful watercolor style that was so pleasing. The best part of the game was easily just looking at the screen. Gameplay and story were meh but the style... *drool*

3. Bioshock Infinite plottwist - This one literally floored me. Legit jaw dropper. Not going to spoiler it if you still haven't played 2013's Bioshock Infinite; but if you have you know what i mean lol. Spent the next few days researching and watching countless youtube videos to explain the story

2. Halo: musical score - Mainly the first three Halo games. But I love the musical score for the franchise. It's the definition of gaming epicness. So much feels. Also going back to Halo 3 and Halo 2 the memories of playing co op with my friends. Good times. Shout out to the underrated Reach which also has an amazing score. 

1. Pokemon Yellow: Fighting Gary after Lance in the Elite Four - Okay so maybe i'm overrating this since i was a little kid. But the moment when you finally beat the Elite four in yellow (you know, that last pokemon game that was actually difficult) then finding out Gary was the real champion? OH AND YOU CAN'T HEAL? Crazy shit. Took me forever to finally beat him. Epic music with that fight as well. 

Your turn. If you're too lazy just do three :p

i cant pinpoint any moment exactly, but xenoblade chronicles had few of goosebumps moment. Super mario galaxy final boss. thats the ones i really got goosebumps from what i remember

i cant pinpoint any moment exactly, but xenoblade chronicles had few of goosebumps moment. Super mario galaxy final boss. thats the ones i really got goosebumps from what i remember

Don't really have a list. But the Ace Attorney games have quite alot of those moments. The Assassin's Creed games as well.

50% of Twilight Princess.

5. Hilda was the culprit!!?? from ALBW.

4. The Nuke from CoD4 MW1.

3.  Just walking around in Skyrim finding random things while listening to the soundtrack.

2. ALMOST beating the final boss of Ninja Gaiden NES. 

1. The final battle from Megaman Zero 4. Zero VS Weil. To his day, the best final boss I've ever played.

Deadly Premonition:
- The Twist in the end

Bayonetta:
- Every Bossfight
- using the hair to see the .... from bayonetta

Alien Isolation:
- Every Encouter with the alien or the androids ("LASSEN SIE MICH IHNEN HELFEN" "SIE DÜRFEN NICHT HIER SEIN")

Asuras Wrath:
- First boss battle against wayzen
- Second boss battle with the one piece music

Metal Gear 3:
- Killing the boss like a boss
- The whole game is just awesome

Spyro year o the dragon:
-The fight with spike

various games collecting the platin like God of War, Deus ex, Bayonetta... ect.

Final Fantasy 8:
- The Opening
- Victory over Omega Weapon
- The End
- The ending (first time) best 25 minutes of my live
- Arriving at Artemisias Schloss
- First Herzensbrecher
- Collecting all gfs
- Catching rinoa in the space
- The whole part in the ragnarok
....

Some breathless moments I can think at the top of my head.

1. Super Mario 64 - Playing it for the first time

2. Mario Galaxy- the moment mario lands on Egg Galaxy and the music starts

3. Smash Bros Melee- Seeing it in action for the first time

4. Chrono Trogger - The title screen, as well as the opening  video

5. Fatal Frame 4- Entering any of the patients' room

Honorable - Skyward Sword- Taking flight into the sky accompanied by excellent music

...And that's what I got so far.

Edit: haha, oops, top 5... Hmm...

5 - My first time defeating Master Hand in the original Smash Bros

4 - Meeting Giratina in the Shadow Dimension in Pokemon Platinum.

3 - Facing Hadron in Custom Robo Arena

2 - Bowser Lifts the Mushroom Kingdom (Opening Scene) in Paper Mario 64

1 - Greil falls to the Black Knight in Fire Emblem: Path of Radiance

edit: Honorable mention to the last stand in Halo Reach

Your spoiler has the wrong game tho, :P