This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Mighty Morphin' Power Rangers
The end of "The Green Candle", by the end the candles' already burned out despite everyone's best efforts and Zordon explains that the only way to prevent the Green Ranger power from being stolen is for Tommy to give the power to another Ranger. So Tommy chooses Jason, who gets the Dragon Dagger and shield. Tommy demorphs. Tommy puts on a brave face but you can tell the failure to protect his Ranger powers hit him pretty hard.
It's just as hard for Jason, who blames himself for not getting the candle when he had the chance. And it haunts him for a long time until "Missing Green".
From the "Green No More" two-parter, the scene when Goldar appears and then shows the already dejected Tommy footage of when he was the powerful Green Ranger (some of it being from when he was still evil, thanks Goldar).
When Rito destroyed the Thunder Megazord Season Three episode "Ninja Quest", that was the last time we ever got to see the original Dinozords in action.
All the times that it appeared that the Zords had been destroyed. While Word of God has said that the "Mighty Morphin" Zords aren't sentient like their Japanese counterparts, those cries sure seemed to have a lot of emotion in them.
To make things worse, there are times where the Dinozords are referred to like they're sentient: Zordon calls Titanus an old friend in "Gung-Ho" and describes the Dragonzord as sleeping when Clone!Tommy is trying to revive it in "Return of the Green Ranger" which suggests that not only are the Dinozords sentient, but that the Thunder Megazord is sentient too. Unless the Dinozords' conversion into their thunder-forms essentially kills them every time.
In "Green With Evil", each part has it's moments. The most heartbreaking one would have to be when Tommy destroys the command center. Zordon, knowing well that Tommy is the Green Ranger, tries to talk him out of it, but to no avail.
Zordon: Tommy, she (Rita) has you under an evil spell, let me help. I can save you.
Tommy/Green Ranger: Worry about saving yourself old man!!!
The destruction of the Command Center. For three years, it'd been the Power Rangers home base, and in the space of five minutes, it's blown up with the Rangers utterly powerless to stop it and seemingly with Zordon and Alpha still inside. Sure, next season, it's rebuilt as the Power Chamber and Zordon and Alpha survive, but it still means that the series is ending on one of the biggest downer moments ever.
A Real Life example: The apparent bad blood between Austin St. John and Jason David Frank, considering Jason and Tommy's friendship.