This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Samurai Jack
"Jack and the Warrior Woman." Sure, most viewers were certain that Ikra was evil and was going to betray Jack, but that almost made it worse! The audience guessed it, Jack could have guessed it, he really should have known: his loneliness and his compassion were both expertly exploited. Akurubbing salt in the wound doesn't help, either.
Jack and Lava Monster features Jack fighting his way through a maze of death only to confront a near-invincible giant lava monster. Then we learn that the lava monster was actually a Viking warrior, imprisoned by Aku in solid stone. He learned to form the stone around him into a monstrous body, and can only be freed to enter Valhalla if defeated by another warrior in honorable combat. Which Jack does, sending the fallen Viking on to eternal rest.
The despondency of the Wild Man and Tribe when talking about the Red Gorillas who make their lives a living hell, and apparently FOLLOW them just so they can steal their food and destroy their home. This is especially poignant if you've ever dealt with an opressor who just WILL. NOT. STOP.
Wild Man: We peaceful like flower, know not how to protect ourselves... OTHER TRIBE TAKE FOOD, SMASH HOME, NEVER LEAVE US ALONE!!! ... we pick up pieces, replant somewhere else. We scared... now like before, we find new home...
Jack coming across the razed villages in "Jack and the Ultra-robots", especially since the first two have one remaining survivor tell Jack what happened before apparently dying. The third village has no survivors left to tell the tale to Jack, so he instead looks at the denizens' corpses and has tragic Imagine Spots of how the Ultra-robots' victims died.
The ending to "Jack and the Mountain Monks.":
Monk: "Have you forgotten!!??"
Jack: No. I have not forgotten.
Even the early parts of that episode are heart-wrenching. At a few points Jack just sounds so defeated.
Jack: It... is... impossible.
"Jack Remembers the Past" is heartbreaking.
The worst part is when he sees his family crest on the bell, and he realizes where he is and starts crying.
"Jack And the Spartans" is full of Tear Jerker moments.
"Your numbers have dwindled. I fear you will not survive another attack..."
"No my king! We will never give up! We WILL FIGHT!!"
"But I must be by your side..."
"No my son, if something happens to me... you will be king". "I will not fail you father."
Note that Jack said the exact same thing to his father in the first episode.
The Spartan King mentions that he is the fifth ruler to fight in the war. That is likely decades of fighting in a HopelessForever War, again, and again, and again, while your neighbors are destroyed one by one, by an enemy you cannot permanently defeat. And there is no hope, no hope at all...
The Spartan King snapping at Jack over his assistance, then immediately apologizing for his insolent tone. Even a Spartan spirit cannot hold forever...
The Spartan Prince taking his father's place on the front lines, not knowing if he will ever return.
"Jack and the Travelling Creatures". After the whole episode Jack had spent traveling, passing test after test to prove his worth, he finally stands before the real, genuine time portal. There is a guardian in front of it and Jack humbly asks to be allowed to use it and is denied. He sounds so jaded after he realizes that he has to fight yet again.
Jack: "I had hoped that just once, I would not have to battle for my goal, because it is noble and just. But I see that this is impossible."
After the guardian Curb Stomps him, he decides not to kill him after all. "You can't use it yet, Samurai Jack. Not yet... Not yet."
In "The Aku Infection", while Jack is trying to fight the illness within him, his spirit, represented as a young boy, meets with his parents. They try to console him, and finally he says in a very quiet, broken voice: "I was not there for you." - In this moment, you realize that in spite of him not making a spectacle of it, Jack is wrecked with guilt about having failed to protect his loved ones.
The ending of "Princess and the Bounty Hunters" was particularly heart-wrenching. Princess Mira, an Anti-Villain who actually has a noble reason to claim the bounty on Jack (so that she can free the oppressed people of her country), works hard the entire episode to set up a well-laid trap. In the end, Jack Curb Stomps the bounty hunters, leaving her as the only survivor. When she realizes she can't defeat Jack, she drops her weapon and cries, solemnly accepting that she can never save her people. It's sad to see her so tragically accept this fate. Though he knows he didn't kill her, Jack doesn't even acknowledge her presence or offer to help her. What's especially poignant is that, knowing Jack like we do, he would have gladly helped her. All she had to do was ask! But she's too filled with pride to do so.
Near the end of episode L (#50), when X9, now powering down, and dying, asks Jack to take care of Lulu. Cue Jack showing a worried expression at possibly killing a perfectly innocent robot.
Made all the more worse knowing that you, as a viewer, could predict the ending before it transpired. It was only a matter of time before Jack got the drop on X9 and slew him. What makes it worse? That it's a Deconstruction story told from the perspective of a random robotic mook who had a life and an existence up until he was taken out by Jack. A Mook Horror Show done as a tragic noir tale. "Lulu... sweet thing."
Jack's sword doesn't hurt the innocent. Either it saw X9 as guilty, or... it does not recognize machines.
That's the thing, X9 was not innocent; he had killed in anger and on orders before. Lulu was his Morality Pet. But that was not enough to save him...
It is possible the writers forgot/did not take in account the magical property of Jack's sword in this story. Also, while X-9 was once a Professional Killer, he regretted his actions, deciding to change; if "Innocent" meant being Incorruptible Pure Pureness who never committed an immoral act, no one, not even Jack, could survive the blade.
Re-watching the episode where Aku tried slaying Jack with his own sword, it seems the exact phrase was "The sword cannot be used to harm innocents IN THE HANDS OF EVIL", which might explain how in "The Aku Infection" episode, Jack slaughtered a seemingly innocent robot while under the influence of Aku, but while still retaining enough of his noble personality.
X9 was fully aware of the chances he had, and still did it because a life without Lulu was a life he didn't want to live. Doubly so because he mentions that the only reason he's the last of the X-series is because he had self-preservation instincts, he loves Lulu so much that it overrode his self preservation. It's fitting that his last line is to beg Jack to save her; even if it means he'll never see her in the afterlife, he wanted that little dog to live.
The Season 5 trailer reveals just how bleak things have gotten during the Time Skip. Jack has been trapped in the future for over 50 years but is still no closer to finding his way home and setting things right, while Aku's rule over Earth has gotten even more oppressive despite Jack's best efforts. Small wonder then that if this line is an indicator, Jack has gone well past the Despair Event Horizon:
Jack: There is no way home! There is nothing to fight for!
A good bit of the beginning of "The Birth of Evil" has the evil that would become Aku mindlessly inflicting these on the world, first destroying the dinosaurs on its landing, then killing a family of cavemen who were just trying to save one of their own, then absorbing an innocent farmer's dog. We get to see the unfortunate man discover his pet's fate, and his cries of anguish are heartbreaking.