A woman blamed Fin for her daughter's drug addiction
Law & Order: SVU Season 6 Episode 10 "Haunted" is one of the reasons it's so sad that Fin gets so little airtime in later seasons of SVU. This story not only provided his backstory, but was fraught with emotion -- and his desire to make amends to a former suspect was heartwrenching.
Benson rescued the little girl that no one believed existed.
Law & Order: Season 7 Episode 3 "911" won Mariska Hargitay an Emmy award, and with good reason. Benson's refusal to give up on a child in need, even when everyone else thought it was a prank caller wasting her time, paid off when she finally was able to locate and rescue the girl, who had been buried alive and wouldn't have survived otherwise. Talk about a tearjerker ending!
A pregnant girl resorted to desperate measures.
Viewers may disagree about whether abortion should be legal, but it would be hard not to shed a tear over the desperate measures this girl went to in order to terminate her pregnancy on Law & Order: Season 7 Episode 9 "Rockabye" and what happened to her as a result.
A dying gangster's daughter pays a visit.
Deathbed reconciliations are always emotional, but the one on Law & Order: SVU Season 8 Episode 10 "Scheherazade" was doubly so because the dying person was far from pure and his daughter had good reason to stay away, yet she eventually decided to go see him one last time.
A reconciliation leads to new life.
The Stabler/Kathy relationship played with viewers' emotions throughout the first 12 years of SVU, leaving some viewers wishing Stabler would leave Kathy for Benson. But Stabler was clearly lost without his family when his wife left him and took the kids with her, and for him to discover he was having another child right after they reconciled on Law & Order: Season 8 Episode 22 "Screwed" was super emotional.
Kathleen Stabler's bipolar disorder.
Law & Order: SVU Season 10 Episode 3 "Swing" was an unusual episode in that the only criminal act was Stabler's daughter Kathleen breaking into a couple's home to take a shower (and a pendant that didn't belong to her). This whole story was a tearjerker, from Stabler's visit to his estranged mother and his making the difficult decision to allow his daughter to be arrested to Kathleen's conversation with her grandmother and eventual decision to get on medication.