Pretty much every time someone is nearly driven over the Despair Event Horizon by a Phantom, with their cracking bodies a visual note to their soul-crushing loss about to take over them.
As well as those who already became a phantom. The Lizardman is a noteworthy example.
Shunpei, Wajima, and the Donut Hungry Shop assistant's crying scene in #7, while actually a funny scene in its own right, could count as this for anyone who's ever went through what those three went through.
#15's ending. After the sheer awesomeness that was Water Dragon's debut, we got a very heartwarming and sad moment with Chizuru watching the film she was in.
#19's after-battle climax shows us the saved Gate, a painter still pining for his deceased wife, sobbing and clutching her portrait, damaged by the Phantom and driving him to almost unleashing his own Phantom prior. Lamenting how his last hope was gone, Haruto then whips out the hitherto-concealed letter from his wife behind the portrait (which his wife left before she passed away). Her letter asks him to live onand paint more paintings in memory of her. It should definitely strike a chord in all widows/widowers and anyone who lost their closest beloved.
#20 shows us what Yugo, Phoenix's human host, was like. Given that the original was such a kindhearted, gentle man... seeing the brutal monster that stole his life and identity just became a lot more depressing.
In #24 we see Kosuke first interrupting someone. It was his own grandmother, who he always saw as someone that would nag him. Even worse, that was the last time he saw her, because after that he found the Beast Driver.
And then his grandmother shows that she genuinely loves him. How? Offering to let herself be turned into a Phantom so Beast can consume her. Just the thought of that potentially happening is heartrending.
And the preview; Kosuke states that if anything ever happened to his grandmother, it would send him into despair.
#25 has Nitoh saying the above line, after the realization that the only reason his grandmother was so hard on him was to protect him. The two share a hug that'd warm the coldest heart.
A second one at the end, where his grandmother learns that in addition to the charm she had given Nitoh during the episode, he had kept the one she had given him years earlier.
#26, full stop. The revelation that your long-lost twin sister is now a monster. Poor Mayu...
It gets worse in #27, after Mayu reveals how Misa was such a loving sister; she receives a message from Medusa requesting them to meet. Medusa then gloats that she was the one who killed their parents (complete with a flashback) before crushing Mayu's memento into pieces right in front of her. The sight of Mayu on her knees, crying out for her parents, is heartbreaking.
#31 has Haruto and Koyomi talk to each other about how important they are to each other, and Koyomi thanking Haruto for giving her hope through his kindness. This scene becomes heartbreaking thanks to Haruto no longer having magic, meaning he can no longer supply Koyomi who desperately needs it, or she will soon die.
Gremlin's backstory, as explained in #35, can be one. The girl he loved broke his heart and betrayed him, leaving him so desperate that he went insane and took it out on everyone who reminded him of the girl that betrayed him. This can especially hit close to home for someone who has been hurt by someone close to them, and can be jarring for people who have let that turn them sour.
#43: Haruto finding out about Koyomi's past, turns out she's the daughter of Fueki, AKA the White Wizard. Which makes one wonder why he left his daughter with Haruto after the Sabbath.
#47: Despite all her crimes and her cruel nature, Medusa's utter heartbreak as she realises Wiseman betrayed her before she dies is surprisingly moving. She's still an Asshole Victim, but still.
#48: Yuzuru becoming the second Kamen Rider Mage, sending all of Kosuke's efforts to help him not be a wizard in vain.
#49: Kosuke damaging the BeastDriver so Beast Chimera could emerge and save all of Tokyo. After that, Beast Chimera leaves Kosuke, kinda sad when you think about it.
#50: The deaths of Fueki and Koyomi.
#51: Really the whole thing is a tearjerker. Everyone's mourning of the deayh of Koyomi. Especially Haruto's
There's one when Haruto finally shows up to fight. He doesn't specify that he wants to save Koyomi's spirit, and this causes Rinko to think Haruto's going down the same path as Fueki. It's sad because Rinko has trusted on Haruto since day one, and her thinking that he's gone bad is sad.