Two of my favorite moments contain very mild world spoilers. If you've crossed the bridge over Lake Hylia, you'll probably know already.
Anyway, the first time I encountered Farosh, the lightning dragon was a real sight. I was crossing the bidge over Lake Hylia when i noticed this enormous dragon, many times larger than the dragons in Skyrim or indeed nearly any other game I can think of, especially as a creature you encounter out in the world rather than a scripted boss. I was in awe and petrified, trying to figure out if it was a boss or not. Eventually I realized he didn't even notice me I was so mall. But then when walking along the shore of the lake. I suddenly died and one of my fairies was used up. I looked behind me to see what had killed me and saw an aura of electricity surrounding the very near by head of Farosh and balls of lightning coming at me to kill me. Scared me to death but was awesome at the same time. What made this amazing was the lack of cutscenes, of telegraphing. I didn't just encounter a god-like beast as large as the bridge I was crossing, it was an un-heralded discovery. It's that element, the games willingness to let you discover such moments rather than walk you to them, that makes Hyrule truly feel like a world absolutely filled with wonders.
Second was also with Farosh, but this was much later when he couldn't one hit kill me. I had learned I needed a shard of his horn to upgrade a piece of equipment. This meant getting a position where I could get a clean shot of his head without dying. So I camped at a lake in the tropical region near a waterfall I knew he flew over. When the time came he burst out of the lake right in front of me and began to fly down just in front of the waterfalls. I jumped off the cliff next to the falls and paraglided over him, dodging balls of lightning until I was in position. Pulled out my bow and I had one shot to get what I needed because 1) he would leave after I hit him and if I missed and got a scale I would have to try again and 2) I was surrounded by like ten balls of lightning that were closing in from all sides :P. Managed to land the shot right before I got zapped and plummeted down into the water thankfully. Lost half my health but got the goods and it was insanely awesome.
The fact the game lets moments of that epicness happen out and about rather than saving all the really cool stuff for story lines is awesome really.
