The building of the World itself. The Lovely World started out as a cold, snowy, barren wasteland, for the most part, but looking at it now in all of its colourful glory makes everything seem so much more impressive, especially due to the fact that essentially everything was built in survival mode, not creative.
Any time Stampy manages to make some incredibly complex redstone contraption, especially since we have seen his progress in learning redstone from the very start... from iron doors to colour-changing floors to far, far more. What makes this even more impressive is the fact that Stampy — according to his Behind the Scenes videos — doesn't rely on tutorials to make redstone mechanisms, meaning his redstone skill is mostly self-taught.
Episode-specific
Episode 124, "Sinking Feeling", is just one long Moment of Awesome, from the epic battle between the S.S. Stumpy and Hit The Target's ship and the reveal that the all-powerful Kraken was secretly Squid, to Hit The Target walking the plank. There's a reason that this is Stampy's most viewed video.
Episode 355, "Friends and Foes": Stampy and William Beaver defeating the Wither together, especially since Stampy wasn't even prepared to fight the Wither that episode.
Episode 500, "Memories": While the reasonhe did so falls into the tearjerker category, Stampy manages to kill Hit The Target almost effortlessly. Not only does this show how far he's come since "Clone Calamity" (where he needed help to take down HTT's clones), but also how much of a legitimate threat he would be if he wasn't holding back in hopes of HTT or Veeva Dash pulling a Heel–Face Turn.
Episode 541, "I Lost": A villainous one — HTT managing to come up with a plan so convoluted that he manages to force his enemy to surrender. This is one of the only episodes that has ended on a Downer Ending so far.
Episode 542, "Hero Helpers": The Helpers managing to rescue Stampy. Polly and Fizzy working together to trap HTT in a pit, while William infiltrates the fortress to get to Stampy, and Polly finally using her redstone expertise to disassemble the trap holding Stampy and Barnaby prisoner.
Episode 670, "Hacked":
Veeva Dash being able to use redstone so well that she broke the in-universe fourth wall.
Episode 679, "Enderman Horde": Stampy and William defeating the Ender Dragon together.
Episode 700, "Tragic Day":
Stampy alone against HitTheTarget, Veeva Dash, and about seven other dogs... the latter of which Stampy eventually takes out, to the point that the two villains had to rush away to get more dogs. This then culminates into...
Stampy and 9 of his dogs (his whole pack except Barnaby) versus HitTheTarget, Veeva Dash, and at least 30dogs. Stampy wins... though not without casualties.
Others
'Stampy's "Lovelier" World' in itself is this — a small build team recreating and revamping the entire Lovely World to the point that it is recognizable, yet completely new. The world includes new mechanics introduced in later updates, plenty of redesigns, and updates minigames which were rendered unplayable in the past so that they can be playable again. It goes to the point that Stampy himself thinks he is Overshadowed by Awesome.
The same build team had apparently rebuilt the entire world almost block-to-block, albeit in creative mode; and is working on rebuilding the entire world again in survival mode.
