Tales of Berseria is doing it to me a lot. Best Tales game ever by a long shot.

Not a big deal today, but the Omaha Beach section in Medal of Honor.

The first time encountering a capital ship in I-War2.

First mission in Wing Commander. Who cares what the mission was: Wing Commander - at the time - was a revelation for me. Bonus that it ran decently on the '286 I had at the time.

First time getting a twinge of vertigo in a first-person game.

For me in that game was Navarro base. The feeling being behind enemy lines, with soldiers in power amour and with plasma gun

Thrilling

In TIE Fighter when you're in the zone, and feeling like you really ARE an Imperial pilot, they run that cutscene showing your craft being launched out of a bay, then add a short hyperspace launch, with a camera view of you dropping out...
Gets you psyched and a shiver down your spine, and that swell of pride when you've accomplished the mission and got praises for your work. Lol. Those were good times.

Reminds me when I first played Wing Comander. That launch sequence had me jazzed.

But I thought that tingling happened when a game had you sit for long periods of time and your limbs start going numb ;-)

At all times that I got that tingly, or shiver rush that spreads out to goosebumps, the music played a pivotal role. It was sound and visual stimulation combined that gave me that sensation. Endorphin rush perhaps?

Arranging incestuous marriages in Crusader Kings 2.

Though in all honesty, that may've just been because I was rubbing my nipples at the time.

Endorphin rush I believe. See Frisson https://en.m.wikipedia.org/wiki/Frisson

Can think of three good examples I think, and in each case the music makes the experience.

Blade Runner - stepping out onto your apartment's balcony.
Unreal - stepping out of Vortrex Rikers for the first time and seeing the alien landscape of Na-pali for the first time.
WoW - leaving Northshire abbey and entering Elwynn Forest for the first time.

Found an impressive remake of the unreal one : https://www.youtube.com/watch?v=muOLx1tPLMI

Wow, I didn't realise it was so deeply studied. Now that I look at it, every example I provided (except the Fallout 3 one, where I don't remember the music, really, but it could've been that too), involved "passages of music and passages that violate some level of musical expectation".

Such things have probably intentionally been designed for.

I think this is a great example! The intro totally does it for me.

Also, exploring ruins and secret places in any Indiana Jones game.

I get this feeling usually because of the music accompanying the situation. Be it epic or emotional.

The final level in Serious Sam 3 comes to mind (especially the boss fight).

Unreal 1 with some huge open levels and the wondrous music made me just stop and observe the surroundings quite often or walk slowly and soak in the atmosphere.

Urzael fight in Diablo 3. One of the few good things about that game.

Final fight in Overlord 1. Also just looking at your character when he is in full Arcanite armor. Just pure badassery.

And many others.

I usually experience it at narrative payoffs. It doesn't seem to be tied to unexpected emotional events, I'm quite likely to have it when I see where the story is going, and it gets confirmed in a "big reveal".

The music is never really memorable, probably because I'm focusing on the events, but it definitely helps trigger it subconsciously.

We're entering spoiler territory here for a few games...

INSIDE - When you get sucked into the Huddle and break free from the tank.
Little Nightmares - After your diet gets progressively worse and worse at periods of hunger, one of the cute cone-headed guys offers you a sausage. You just know what will happen a few seconds before, then BAM!
Deadlight - At the end of the story, however predictable it was at that point.
Sanitarium - Can't recall the exact moments, but it was several times, usually at the end of the chapters when you piece an emotional memory together. Brilliant game.
Diablo 3 - Act IV intro video when Leah turns into Diablo. Dumm-dumm! Completely predictable and a few hundred grinding hours later you don't really give a crap about any of those characters, but the first time was somehow different.

Hm ...

Bioshock Infinite: Welcome Scene in the beginning. I just stood there for a while, awe-struck, overwhelmed by the solemnity, gazing at the halls, listening to the sacral choirs, feeling a mixture of wonder, calm and unease.

Diving in Abzu and Subnautica, marveling at the colorful scenery, listening to the relaxing sounds and music, seeing something huge swim by in the distance or suddenly hearing a scary noise for the first time.

Crypts in Arx Fatalis. Atmosphere was so good, it really creeped me out. Usually crypts are nothing special in RPGs and seldom scary, but this one was, even after I saw through how it was scripted. It actually made me a bit hesitant to move forward. :D (The sound design is pretty good overall, in other levels as well.)

Oh, I see. Well, [mild spoilers] in Hollow Knight I had this feeling early on, when I saw how beautiful every detail is drawn. Then I went into the first bigger area and realized how much work has been put into crafting that game. Later on I got the first skill, that allowed me to backtrack to the starting area and I realized, that there wasn´t just some hidden item to find, but a huge new area to explore. And these moments when you realize, that you get more than you expect go on and on until the very end of the game.

[mild spoilers end]