Simply Pokemon episodes or scenes from a particular episode that make you want to grab a tissue for me there are a few
-Bye, Bye Butterfree; just sad to see Ash let go of his first capture. Saying that he would tell the other Pokemon that it was just on a vacation was what got me balling like a baby
-Pikachu's Goodbye; after telling Pikachu he belonged in a forest, turned away and started running along with the montage with "The Time Has Come" or whatever that song title was just made me lose it. Then with the sun rising and Pikachu is up on the hill, says goodbye to the wild Pikachu, runs into Ash's arms and he starts crying...just powerful stuff right there
-Charizard's Burning Ambitions; After Charla threw him in the water, Charizard emerges. That look on his face and the background music was just heart wrenching! I think Charizard was actually tearing up (It was hard to tell because he was covered with water) before roaring really loud with Liza shut the entrance to the valley. Then Ash having that heart to heart the night before he leaves him behind. Charizard was just standing there in the water, and crying with Meowth doing a translation was touching, not to mention Team Rocket throwing rocks at it during the night to keep it awake so its tail wouldn't get completely wet when going underwater and even faking an attack in a robot on the valley to get Charizard's ambition going again
I think this is my favorite in the category when Ash was talking about how he knows what it feels like to not feel good enough and I can relate. That was just one that stood out to me.
-Gotta Catch You Later! Misty actually showing emotion over leaving Ash showing their "relationship" and the episode itself because we say goodbye to the original trio...
-Pikachu vs. Latios; Yes, this one made the list and I didn't put the episode because I just like THIS scene. It shows the relationship of Ash and Pikachu being far above what it once was. Remember when Pikachu didn't want to fight Sabrina's Kadabra after getting beat or when it was too scared to fight Surge's Raichu (in both cases Pikachu eventually puts aside fear to help out Ash), but in this case here is a legendary Pokemon and Pikachu doesn't think twice about going in there as Ash's last resort!
Honestly, after Johto there were not a lot of emotional moments for me probably due to the show repeating scenarios from previous seasons or the characters honestly not being that interesting.
There are a few more in my list but these were the ones that stuck out to me the most.