I feel like most of my favorite Pokémon anime parts are mostly in the movies or shorts before it; or just parts of episodes. 
And since @lyleberr already described one of my favorite episodes that came to mind first in his spoiler, I’ll go with another one of my favorite episodes:
In an episode where Pikachu pretends to be asleep since he’s too afraid to battle; Charmander almost breaks its back after another Pokémon jumps on top of it; and Ash burns his hand, our protagonist is encouraged to burn his hand yet again after a girl breaks her arm.
The day after, Ash and two other people almost die after being caught up in an explosion. After that, another person and their Pokémon do actually die by drowning in the river. Followed by yet another explosion, thanks to flammable gas, causing two more people and their Pokémon to fly off into the distant (although they defintely won’t die, since it’s Team Rocket, who’ve become immune to those kind of explosions and high altitude falls after experiencing it so many times before).
After the Pokémon Ash borrowed almost loses an eye thanks to 1/3rd of a bird, he still manages to finish first, after that between his legs turns white, which made the girl with the broken arm very satisfied. It’s not called the Big P Pokémon Race for nothing, folks! 
EP033 The Flame Pokémon-athon!, and the Big P Pokémon Race is the actual name of that race, haha. 
Greetz,
Quuador