I wouldn't say it's the saddest moment for me, but the most heart tugging one for me is in the first episode where Ash was willing to sacrifice himself for Pikachu, showing Pikachu that Ash was legitimately good and cared more for him than himself.
EDIT: Also, "Gotta Catch Ya Later" was very sad when the original trio (Ash, Misty, and Brock) finally broke up. As a kid, I remember shedding tears when they left, but even more when Ash was all alone in the hole Team Rocket trapped him in, and he used the things Brock and Misty had given him overcome the poison gas they had used and to climb out of the hole saying how he'll always have his friends. And even when Gary left! Of all people, I never thought I'd actually care about him too.
I'd say after "Gotta Catch Ya Later" a good part of my childhood died that day, and Pokemon was never the same again for me.
End rant.