In Slayers NEXT, it's almost impossible to not feel bad for little Amelia when she thinks her dad is dead (he's just faked his death to uncover a complot, but she doesn't know that yet) and breaks down crying in Phil's library as she finds the book that her dad used to read to her when she was a little girl. That one was so sad that even Lina got briefly depressed and gave her a hug before promising to help her through all of this.
When Amelia is nearly killed by Gaav, and later temporarily IS killed by Hellmaster. Zelgadis' reactions, both times, make them extra painful.
In TRY, when Valgaav dies at the end. Even though he's reborn, the only character who isn't depressed by this is, of course, Xellos.
In Slayers Next, right after Lina defeats Phibrizzo, and everyone is waking up only to find that "Lina" does not exist anymore. The way that Gourry stands there watching her and then says "I don't know what's going on- but you are taking Lina away, I want it undone! I WANT IT UNDONE!" And everyone joining in to tell off the Lord of Nightmares.
In episode seven of NEXT, a chef tells Amelia that he wants to help her and her friends catch the dragon and make dragon cuisine because he was unable to make some for his late granddaughter, who looks like Amelia. It turns out that he told every member of the group the same story, telling Lina that she looked like his dead daughter, that Gourry looked like his dead son-in-law, and that poor Zelgadis looked like his wife. At first it seems like it's a false tearjerker meant to get a laugh, then we find out at the end that he was telling the truth, due to him having a locket with a picture of his family. If you watch that scene again and now know he's telling the truth, you may be inclined to tear right back up, especially with the music playing during the scene.
Gaav's Kick the Dog moment in which he verbally brutalizes Amelia, then tries to kill her... and Zelgadis goes Taking the Bullet to protect her, which causes the poor girl an Heroic BSOD as he bleeds to almost death in her arms. That was so freaking sad.
The opening to the 23rd episode of NEXT. Gaav's dead, but Phibrizzo has revealed himself and taken Gourry away with him. Lina wakes up, remembers what happened the previous day and the reality hits her that Gourry is gone. She then notices that there's something falling on her lap and realizes it's her own tears; the whole time she's started crying. And then immediately after that she collapses into full blown sobs.
Episode 10 of Evolution-R, when we discover from Rezo that it is impossible for Zelgadis to restore his body. Zelgadis' agony is heartfelt and sells in both languages...he even cries for the very first time in any form of media!