Vanilla: I have 2 here, First was my first time finding an abomination wandering down to Darkshire wrecking everything in it's path. It was still early enough in wow that there was no high level toon to destroy it so it got all the way. My second was finally... FINALLY getting the last stage of my Paladin changer quest done, the group was just barely keeping it together at the tail end of the event, but we got it done and I spent the next few days just marveling at my golden armored pony.
BC: For me it had to be finishing up the Neatherwing rep, that just felt like my capstone moment of BC.
WotLK: This one is hard to pick I loved this time of the game so much, A few notable moments for me where the Addition of Stormwind harbor, the Wrathgate, Stormpeaks music, The Gunship battle, and getting to fight Arthas.
Cata: Cata was a mixed bag for me, but it did have a moment or two like Getting to fight on Deathwings back.
MoP: like WotLK this expansion was chalked full of memorable moments, the intro quests, Getting into the vale, TotES, Landfall, island of thunder, SoO.
WoD: (Insert when it was over meme here) Past that I will give WoD some credit, the leveling up experience was cool at points, for me Spires was cool and fun.
Legion: It had a few like moments of the order halls, and going to argus.
BfA: I actually liked this expansion more then most it seems, I liked the intro assault/defense of UC, I liked both of the capstones for each sides story (special props to watching Jaina summoning the fleet) , Warfronts, and the assault on Daz to name a few.