For me personally, in no particular order, my favorite moments in the game were

-The arrival of the Prydwen

-Exploring the Glowing Sea

-The launch of the Constitution

-Getting to the bottom of Dunwich Borers

-The House Cabot questline

-Learning what happened to Vault 81

*and yes, I realize I spelt memorable wrong in the title*

My most epic moment was a fight I had on very hard difficulty. I was doing the BoS questline and was doing the "Lost Patrol" quest. I had a crazy battle with several high lvl Super Mutants at the Satellite Array. My heart was pounding at the end of this fight which took 20 minutes to finish.

The arrival of Prydwen was awesome! The follow up was a bit of a let down.

The memory quest was really cool to me. Made me feel sympathy and wished I could have befriended him. He's my kinda char.