I've been rewatching all the episodes from the beginning (I'm at the end on the Advanced Battle Series now) and I'd say these moments are the best -
1. Ash standing up to face the Spearow in the first episode. Probably the most epic thing he's ever done.
2. Butterfree's goodbye
3. Pikachu's goodbye and return
4. James returning after Jessie and Meowth thought that James has left (in Holy Matrimony)
5. Ash and his Pokemon fighting the cold together
6. Leaving behind Charizard at the valley
7. Ash, Brock and Misty going their separate ways after the Silver Conference