At the end of the flying prince and princess episode when he gave up a opportunity to slay Aku to help the the kids get to their ship that they could get reinforcements to help their people save their home from enemy invaders, he told them how he knew what they were going through and couldn't allow them to fail. At the end they won their war and built a statue to honor and remember Jack.
From that same episode- when the alien Prince and Princess find out that Jack is really a Prince, they bow to him just before they leave and call him 'Your Majesty', acknowledging his royal heritage as a form of respect.
Jack's mother and father coming to him in his hour of need during the end of "The Aku Infection" episode. When Jack felt he was losing to the evil inside him, the spirits of his parents helped remind him of the goodness in him and how it has been strengthened by those he helped since his coming to the future. In the end, he exorcised the evil within him and freed himself. This not only counts as an epic heart warmer but a joyful tear jerker as well.
At the end of "Jack Remembers the Past," a robot villager begs for aid, and Jack, who has spent almost the entire episode lamenting his lost life, drops everything and goes to help without hesitation. As he leaves, we see the spirits of his parents, watching him with proud smiles.
Lulu, sweet thing.
Everything that the Scotsman went through to help an amnesiac Jack. It must have taken days, maybe even weeks to find the source of the problem, but that didn't matter to the Scotsman. All that mattered to him was that a friend of his was in trouble.
Add to this was how amnesiac Jack is vastly different in personality and ability to how he was before, ending with the Scotsman doing what he can to keep him from harm's way. The clincher? He always tries to make an excuse as to why amnesiac Jack is messing up. Remember when they first met? He was almost always finding ways to humiliate or insult Jack. Now? He's thinking of any excuse he can to defend and preserve Jack's honor.
He spends the entire adventure becoming more and more frustrated that he can't find out exactly what happened to Jack, but follows up whatever information he can without even hinting at giving. When he finally encounters what he quickly figures out to be how Jack "lost his brain," he looks at his brain-addled friend with a genuine smile - not a goofy grin like he usually does, but an very heartwarming "we've got 'em now" smile. Then comes the "bring it on" smirk.
When the adventure is done, they spend what is implied to be a very long time just laughing and reminiscing together - the kind of thing Jack barely while trapped in the future. So much time, in fact, that they miss the boats off the island they're trapped on.
Early in Season 1, there's an episode in which Jack tries to rescue a fairy trapped in a magical orb, who will grant one wish in her lifetime. He doesn't realize that what enters the orb cannot leave it, and gets his hand stuck with the fairy (who's trying to give him advice). She explains that he needs the control orb from the golem guardian, and Jack, after much butt-kicking, gets it. Before it expires, the golem looks at Jack's trapped hand and laughs. The fairy explains that the orb will only work with the control word, which only the recently-deceased golem knew, and "Now we'll never be free." Cue pained look from Jack, a moment of despair, and then:
Jack: I wish we were free.
When Jack frees a bunch of teenagers from Aku's Mind Controlling rave music, Olivia and her father's tearful reunion.
Olivia's Father: Olivia?
Combined with a Crowning Moment of Funny, we have Jack telling Da Samurai that he has taken the first step towards becoming a true samurai after the man, up to this point an obnoxious blowhard until Jack deflated him, pushed Jack out of the way and took a bullet, or an energy blast in this case, for him.