Bye-Bye Butterfree (Ash releases Butterfree)
Charizard's Burning Ambitions (Ash leaves Charizard behind)
Gotta Catch Ya Later (Ash, Brock, and Misty go their separate ways)
Pikachu's Goodbye (Ash releases Pikachu but Pikachu returns to him)
Those are definitely the four saddest. Especially Gotta Catch Ya Later. I remember really feeling Ash's pain when they left each other.
Though it was a movie, that famous scene where Ash turned into stone and all the Pokemon near him were crying... I still find myself going emotional when I see that scene, and I usually don't get emotional over this kind of stuff.