In the order that I played them(spoilers ahead of course):
3
I can't think of a particular experience that really stuck with me, but it was more the exploration in general that I loved.
NV
Confronting Benny for the first time was quite satisfying. There was a long buildup leading to that confrontation when I first played New Vegas. I was so ready to shoot that prick in the face. It was great seeing him try to calm me down and reason, but I wasn't having any of that. I heard what he had to say and decided I couldn't trust him and would rather just get vengeance. I was ready to blow him to pieces whether or not I pissed off the Chairmen. It was a fun and gratifying fight. Tearing him apart or screwing him over never cease to give me pleasure.
4
Seeing the Brotherhood airship for the first time after exiting the Cereal Killer's base(Kellog at Fort Hagen) was really breathtaking for me. I didn't know how big of a role the BoS would be playing in Fallout 4 at the time, so seeing the Brotherhood swoop in with a giant zeppelin and a fleet of vertibirds was really memorable. Honestly, I couldn't have cared less about the story in that moment, I was just taken away by the beautiful scene that was so well set up in front of me. I found myself standing still and slowly panning over the scene to take it in. As much as Bethesda failed at the crucial aspects of the game, I really liked that moment.
1
I loved interacting with the Master for the first time. The two voice actors working in tandem to create this ominous, creepy, and somehow relatable character was amazing. I was in awe at how well that character was presented, and the fact that this disgusting, evil antagonist had real motives that I could understand and almost respect. It was an intensely eerie and exciting moment. The Fallout games I had played prior to the original never presented a character so chillingly real or an experience so gripping. I will certainly be playing the original again, even if just for this encounter(there was a lot more I enjoyed and surely a bunch I missed). This was probably my favorite moment of the franchise.
2
I haven't finished the game yet, but I quite enjoyed going behind the First Citizen's back in Vault City to save the ghouls and the city at the same time by working with McClure and the people of Gecko. Lynette was a demanding jerk, but I wasn't going to let that stop me from doing the right thing. I had heard about how much other fans hated the First Citizen, so it was gratifying to circumvent her orders and do right for the ghouls and citizens. I was glad to have at least one kind, rational man to help me in a city full of cynical bigots and bureaucrats. Harold in his classic form was also interesting.