A meta-example: in 1994, TV Guide asked its readers to name the top five romantic couples in the history of television, with the adviso that these couples had to display what was a truly supportive, compassionate, and most of all loving relationship that didn't feel false, forced, or pretended. The readers named Gomez and Morticia Addams as the greatest television marriage ever, with over twice the votes of the second-place couple, Rob and Laura Petrie of The Dick Van Dyke Show.
From the biker episode, the biker dude tells his father, "They may be kooks, but they're MY kinda kooks." After watching countless strangers run in terror from the Addamses, it was surprisingly sweet to meet someone who accepts them (which is, probably, because they are so accepting of him in turn).
This also leads to his father coming to accept him as well.
In the first movie when the family is searching for Wednesday and Gomez finds her asleep in the crypt. Being careful not to wake her, Gomez gently picks her up and carries her back to the house.
Near the end of the second movie, Fester returns to his family and gives Gomez a hug. Wednesday and Pugsley show up as well.
To elaborate, when Wednesday and Pugsley return and see Fester has come back, Pugsley immediately runs to his uncle and hugs him. And while at first it seems like Wednesday's just going to keep out of the tearful reunion and do some more of her famous snarking, eventually she too runs to Fester's arms.
"[Fester] was a good man!" "Is a good man!"
As twisted and Crosses the Line Twice levels of Too Kinky to Torture Morticia and Gomez could be, you couldn't help but smile at scenes between them. All those years, and they're still passionately head over heels for each other.
When Fester asks Gomez to help him woo Debbie in the second movie, Gomez doesn't hesitate to agree. And at dinner, when Fester is so nervous he can't even speak and ends up handing Debbie his half-eaten bun, Morticia lies about that being a quaint French custom. It's just so heartwarming to see how Fester has truly been accepted by the family, and how they will do anything to help him find happiness.
In the second act of The Musical, Gomez sings to Wednesday about his conflicting emotions over her growing up and being engaged ("Happy/Sad").
In the tour version of The Musical, Gomez cuts a tassel off the curtain while fretting over whether to betray Morticia or Wednesday. Cousin Itt ends up marrying that tassle.
In Sweetheart of a Brother from the 90s cartoon, Pugsley drinks a formula which effectively makes him a "normal" person by removing all his quirks. His reasons for doing so is to get his crush to notice him, thinking if he were normal she'd like him better. While his family are indeed shocked by Pugsley's new desire to dust, clean, and forgo the pursuit of inflicting bodily harm on his sister and uncle for laughs, Morticia reminds Gomez that just because he's "different" does not mean they will love him any less, rather than spending the rest of the episode trying to get him to change back. Even if their own children suddenly became like everybody else, Gomez and Morticia would never stop loving them, proving that the two are exceptional parents.
A stark contrast to Addams Family Values, which sees the two panicking over the possibility of their infant son growing up to be an outstanding member of society and Gomez even falling ill because of it.
Similarly, Wednesday was hoping to get Fester to help her turn Pusgely back to the way he was, but her reasons for doing so was that she didn't want Pugsley to give up his individuality, and she'd seen that the new Pugsley is a timid coward. Of course, she didn't actually partake in any schemes to undermine Pugsley's new personality.
Much later, Pugsley snaps out of his "normal" persona after the girl he likes is being berated by the bully Pugsley used to be able to handle until he became normal. His crush was trying to defend Pugsley from the bully. After giving the bully the patented Addams Family treatment, Pugsley's crush states she is happy he's back to being himself, but she's sorry that she's soon heading back to her home country. However, she does ask if she and Pusgely can be friends.
There are also a couple of heartwarming moments in the 90's cartoon during the episode "Double O Honeymoon". It was yet another example of seeing how much Gomez and Morticia truly love each other, but the real heartwarmer is in the ending, where Norman Normanmeyer, the neighbor of the Addams Family who hates them, actually seems to warm up to them after they save him from Ian Thundermane.
In the second movie, Debbie is buried in the Addams Family cemetery. Sure, she tried to kill them, but she's still accepted as an Addams.