I have a ton of them really. WARNING LOTS OF SPOILERS FOLLOW.
1. The death of Lavitz from Legend of the Dragoon
2. The final boss fight from Legend of the Dragoon
EDIT: ...okay, I thought I pressed "preview" Gah!
3. The soldier in the intro to Lost Planet: Extreme Conditions, who does this awesome slide-dash while firing a machine-gun at a giant alien.
4. The cutscene at the end of Lost Planet: Extreme Conditions, when you shoot the main villain.
5. The climb into the well and subsequent escape during the first day of Darkness Within: In Pursuit of Loath Nolder.
6. A ton of moments from the John DeFoe Quadrology, specifically the endings of Trilby's Notes and 6 Days a Sacrifice.
7. When you fight the T-Rex in Peter Jackson's King Kong: The Official Game of the Movie. (God I hate that title...)
8. Myst. Just, all of Myst. It was like the first adventure game I played and had a huge impact.
9. The beginning of Broken Sword: Shadow of the Templars, when the bomb goes off in the café.
10. When Arthur turns into a virus to save your life in The Journeyman Project 2: Buried in Time
11. Fighting Sephiroth in Kingdom Hearts II. That battle is really intense and is just awesome to even watch.
12. Entering Ravenholm in Half-Life 2, as well as Father Grigori's introduction and death, which are just plan epic.
13. 7 Minutes. That whole game was interesting and inspiring.
14. Cactus's Mondo series has always been really neat and I love the ending to Mondo Medicals.
15. Killing any of the Colossi in Shadow of the Colossus.
16. Escaping the exploding ship in Advent Rising, as well as the epilogue fight and cutscene.
There's probably more but those come to mind immediately.
Oh I missed the second part, which is what we can learn from each of these. Numbers line up and so forth. Oh yes, and more spoilers follow.
1. Lavitz was established as being an important main character. He was characterized well and his death came as a surprise because it was so unexpected. (Hey I never played FF7 so I didn't know about the Aerith thing until about the release of Advent Children. >_>)
2. This was simply epic because he had 4 freaking stages, took like 40 minutes to beat, and you fought him AS HE DESTROYED AND RECREATED THE WORLD.
3. Again, moment of epicness. It may also have something to do with the soldier then screaming at the top of his lungs in a totally authentic voice "Die you sons of bitcheeessss!!!!" as he shoots at a monster like 10 times his size. I mean that's just unnecessarily badass, and this guy isn't even an important character! Lesson: Make random soldiers badass, so then EVERYONE is cool.
4. The build-up to this was great and it was an excellent climax. The epilogue ruined it though. Lesson: Epilogues can screw up something awesome.
5. Again, build-up was great. It was described as if the well was a source of something dark and evil, and when you finally got down there the tunnel in the side was caved in. But then as you're ready to turn away SOMETHING STARTS DIGGING THROUGH. So you run the hell out of there as the screen is shifting up and down and a blur affect comes in while your character starts breathing heavily. Lesson: Tension, after being brilliantly built up, CAN be brilliantly used to make things scary/creepy. (Though I'm a pansy so that may explain a lot.
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6. Can't really explain much here. It was just epic and unsettling on some level.
7. The T-Rex is simply unbeatable. The entire fight just sets mood and you're just trying to stave this beast off and distract him as the other two guys open the gate for you all to run through. Lesson: Sometimes an unbeatable boss can be used to increase tension and anxiety.
8. Lesson: Games at an early age can be wonderful and inspiring to later life.
9. The setting was peaceful and quiet, and everything looked so cheery and happy. And then the bomb goes off and you're just thinking "SHIT". Somewhat unnerving. Lesson: Atmosphere is key, and you can make sudden chaos more interesting by establishing order ahead of time.
10. The emotional attachment to Arthur built up through the game due to his wit and commentary. When he leaves, you feel like you're losing the one friend who was with you through the whole thing. And he's essentially sacrificing himself to save you. Lesson: Characterization is key, and sacrificial events can actually have an emotional impact if the proper connection with the player has been established.
11. Yeah I got nothing else to say here.
12. Atmosphere. Lesson: Atmosphere is very helpful.
13. The point of the game was to escape death, and you couldn't. The point of the secret ending is that you shouldn't waste your last minutes of life trying to escape death. Lesson: Deeper meanings can make things more interesting.
14. I'm not gonna explain this one, but it was mainly atmosphere and a "WTF?" moment.
15. These monsters are HUGE, and you have to kill them with your tiny sword, all to save someone's life. It's epic, it's emotional, it's dangerous, it's scary, and it's powerful. What we will do to save someone we love. Lesson: Again, deeper meanings.
16. Just plain epic. Lesson: Epicness is cool.