From "The Day Gomez Failed", seeing Gomez looking so dejected when he feels he's tried everything.
Gomez: "Don't try to cheer me up; it's hopeless! I'm nothing more than a pathetic success of an Addams!"
The scene in "No Ifs, Ands or Butlers" where, after Lurch becomes a cowboy, Thing and the kids have to say goodbye and go home.
Wednesday crying when she thinks her headless doll burned up in the fireplace in "Little Doll Lost".
1964- 1966 series
Morticia crying in "Morticia's Dilemma".
Seeing Wednesday cry over being read a story where a dragon dies.
Wednesday (in tears): "He killed the dragon" Gomez: "Who did?" Wednesday (still tearful): "A knight in shining armour!"
And later, when she's sad in "Wednesday Leaves Home"
Seeing Lurch sad in "Lurch's Little Helper". He even cries at one point.
And he cries several times in "Lurch and His Harpsichord". When you see him burst into tears while looking out the window as the harpsichord is taken away... You will feel like giving the big guy a hug.
Lurch: "Nobody cares about me"
Ophelia could be this sometimes.
Ophelia: "I'm the most miserable person in the world"
Fester being sad in "Fester Goes on a Diet"
His reaction to accidentally spoiling a family trip in "Uncle Fester's Illness"
The whole scene with Gomez attempting to commit suicide in the belief that Morticia is straying with Lionel. Can double as Nightmare Fuel.
This scene with Morticia, who's caught Gomez giving Mildred romance lessons:
Morticia: (after Thing hands her a hankie and she wipes her eyes, this whole quote is said in a tearful voice) "Thank you, Thing...I'm sorry to make a spectacle of myself, Thing, but my world has come down around my ears."
You can't help feeling sorry for Gomez as the Butt-Monkey of this episode.
And also Morticia. She is Gomez's wife and is head-over-heels for him and then he gets amnesia and not only doesn't know who she is, he's outright rude, accusing her and the others of trying to kill him, wanting to chop down Cleopatra (which the whole family considers murder), and wanting her to stop wearing black (which is a major offence if you're Morticia.)
Seeing Fester of all people in a funk when his job fails. Weepy voice, listlessness, lying on his bed, all that malarky.
The two episodes "Morticia the Sculptress" and "Morticia the Writer". Both involve Morticia starting a new hobby and Gomez wondering if she's too busy for him.
Gomez prior to meeting Morticia. He's cynical and a hypochondriac. Thankfully, that went away pretty quick.
In "Cousin Itt and the Vocational Counsellor", Morticia and Gomez are pretending that they are a bickering couple and Cousin Itt is their counsellor. This is funny up until Morticia thinks Gomez really meant one of his lines and starts crying. Even worse is that that night, she won't even let him sleep in his own bed so he sleeps on the couch instead.
The very first lines in the first film as Fridge Horror sets in. The family has been holding a seance for Fester every year for 25 years in hopes of contacting him. A seance is usually invoked to summon the spirit of someone who is dead. When Gomez laments, "And, for 25 years... nothing. I'm beginning to think my brother truly is lost." He was more comforted with the idea that Fester was dead versus being cut off from him forever.
Wednesday and Pugsley begging Fester to come to their play and Fester, in tears, saying "I'm busy". Lessened when he decides to go anyway against his "mother's" wishes.
The Addamses being forced to move out of their home. Each member looks absolutely dejected as they are seen packing up their belongs into the family car. Even Gomez, who played the A Fool for a Client card in court to fight the restraining order, suffers a Heroic BSoD that he takes a good while to recover from as a result of the loss (quite jarring when you remember the Gomez of the series happily shrugging off such losses). Further, as the car pulls away from the house, you can hear Fester — who's been watching them from a window this whole time — crying in the distance.
After they're forced from their home in the first movie and Gomez slips into a lethargic depression, the normally humorous Bait-and-Switch gag formula that's proven itself for laughs so far is used to heartbreaking effect.
Employment Officer: And what about your husband? Is he currently employed? Morticia: He's going through a bad patch at the moment. But it's not his fault. Employment Officer:Of course not. (sighs, annoyed) What is he? A loafer? A hopeless layabout? A shiftless dreamer? Morticia: (choking a little) Not anymore...
As infamously terrible and cheesy as Addams Family Reunion was, it does manage to throw in a surprisingly heart-wrenching scene where Gomez actually breaks down in tears over his parents becoming "normal". Helps that Tim Curry, a very good actor in his own right, decided apparently to take the bad film seriously.
The family's entire situation in Values, culminating in Morticia shedding a Single Tear at Gomez's bedside - possibly her equivalent of uncontrollable sobbing. Their youngest son is ill with a disease that they don't understand. Gomez and Morticia try to make him happy, because they're Good Parents, despite their own distaste. Their long-lost brother was found, only to be driven away from the family again. The grief causes Gomez to start dying. Luckily, the Trauma Conga Line ends rather quickly after that moment.
Downplayed with the Addams' kooky and ooky way of displaying it (as well as Gomez and Morticia being quick to try and quell the anxieties), but Wednesday and Pugsley's anxiety over their family preferring Pubert over them. It's a very relatable fear for many real-world older siblings.
The New Addams Family
Uncle Fester being sad when he's forced to speak in rhymes during "Cleopatra, Green of the Nile". The rhyming downplays it, though.
In "Death Visits the Addams Family", the Grim Reaper comes for Gomez and everyone else is rightly shocked (if still stoic) that Gomez might die. Thankfully, he doesn't die. He probably owes it all to being an Addams.