So I'm merrily playing and I finish the "Lost innocence" quest, since I don't have time to kill I step out of the house I'm in and immediately fast travel to the Riften stables to be approached by a courier as soon as the game loads, I am handed a mysterious note and I decide to read it right away.

Keep following the SPOILER quest line. It gets better ;)

My favourite Skyrim moment is actually a Youtube video that someone posted. Everything about this video is golden. From the French language to how amazing the AI unravels infront of you. To the fact that the guy strips the man naked and picks back up his lettuces.

I have also had a horse fall out of the sky and land in front of me, then proceed to slide down a mountain into a bandit camp.

@Ravenlight said:

Keep following the SPOILER quest line. It gets better ;)

I've just started that!

For me it was having lydia die in Fort Dunstad and then only to find her body naked surround by a huddled screaming group of other NPC's just inside the front gate of Whiterun. I have no idea how she got there, but I was just as freaked out by it as those NPC's were.

A Giant thwapped Lydia and she went skyrocketing ten times faster and farther than your own body normally does. I lost her for about a half-hour, then as I was fighting a dragon, near death, she came and pulled aggro for me. 
 
At the intro sequence, the horse started spinning in circles, and the cart kept tipping over sideways and then straightening back up at ridiculous speeds, all the while everyone's just carrying on conversations like nothing's wrong. It ended with Ulfric and the horse thief being stuck behind a fence, unable to find their pathing to their cutscene triggers. Had to restart, but  worth it.

I was attacked by an Elder Dragon, whose texture did not load and so I was fighting a giant urgled blob of a dragon. Funny still was that texture an extremely dark black, and then when he died he turned into this bright golden brown.
 
Also, a couple of hours before the Elder Dragon fight, I was roaming along and ohhh no, a Dragon. Wait, not just one Dragon... TWO OF THEM! As I was fighting one, the other one somehow managed to crash land and... Break his neck? He did that swan-dive thing they do and died instantly. I didn't see him hit, but I looked over to see his ass aiming right into the sky, but his neck all twisted and lanky. It was pretty funny.