When Peter is too sick to have Thanksgiving dinner with the rest of the family, they wait a day to have Thanksgiving dinner so that he can eat it with them. Andy's line of "Call us your family" has been known to cause people to get a bit of sand in their eye. See it here.
A strip from July 1989 where Peter tells Denise what it is he likes about her:
Peter: Denise, you know why I like you? You're not phony. You're bright... You're funny... You're a knockout... You make me laugh... You make me think... You make me feel special... You're honest... You're caring... You're forgiving... You're silly... You're perfect. So what do you like about me? Denise: Your terrific taste in women. Peter: Really?! Thank you. Denise:[kisses him] Thank you, Peter.
The two times that Jason expressed honest love for his parents: first with his mother at the beginning of the summer camp arc in 1997, and again in a storyline after 9/11 where he admires Roger for mustering the courage to give blood.
There is a sweet (surprisingly not squick-inducing) story where Paige can't find a date to the prom, and Peter is stiffed by Denise at the last minute. Andy suggests Peter take Paige, and though he goes through the requisite feelings of humiliation, in the end Paige has a great time and genuinely thanks him. It's warm-and-fuzzy, genuine brother/sister moments like that that made the early years of the strip so great.
Father's Day 2011; Jason makes Roger a comic book about "Super Dad" as a gift, saying he could give better gifts, like golf clubs, or a Ferrari, if he had a bigger allowance. Roger calls the comic the best gift ever. Yes, even by comparison to a Ferrari.
Considering Jason was using the comic in an attempt to tell Roger he should give him a bigger allowence, it's also a case of Comically Missing the Point.
One comic has Jason show Quincy a magic eye picture that reads "Jason is your best friend." Jason muses that it would be better if Quincy could read, however Quincy's tail is visibly wagging.
In one one-week arc, Roger takes Paige shopping:
Roger, thinking:(fuming) 9 hours in the mall! Why did I agree to this?
Paige:(leans over and kisses him on the cheek) Thank you, Daddy!
Roger, thinking:(now smiling) Ah, yes...
The week-long arc where Roger is depressed over turning 45. What finally snaps him out of it? Andy kissing him. Then, the two proceed to exchange kisses.
Any strip where Jason treats Quincy as an actual pet rather than as a mere prop to annoy his family with. One of the best of these strips is where he and Quincy make up after Quincy destroys Jason's very first Slugman comic. The reader doesn't even see Jason's face and the effect still works; the fact that it works show just how simple and sweet their affection for each other really is.
Quincy, looking uncharacteristically aware that he's done something wrong, licks Jason's face from a distance.
Jason is now lovingly holding Quincy, who has resumed licking his face.
The mother's day strip where Quincy gives Andy a dead cricket he'd been carrying in his mouth (although she fails to understand why). That's right; Jason's pet iguana not only views her as its mother, but clearly loves her as well.
The Christmas storyline from 1997, where Andy's mom comes for a visit. Actually provided a nice development for Andy.
To specify, the storyline begins with it being clear that everyone Andy has known has loved her mother, leaving her feeling inadequate and resentful. Andy does her best to hide this, but finally accidentally blurts this all out while her mother is standing behind her. Hearing this, her mother sits down and hears her out, letting Andy explain why she's so miserable. When it's time for her mother to leave, Andy sincerely asks her back for the next holiday, and is pleasantly surprised to find she isn't feeling horrible at the thought.
In an early week-long arc, Jason is embarrassed to go back to school because Andy got him a Garfield binder, so he goes to the first day of school wearing a sack over his head. There, he sees a girl who's also wearing a sack over her head, and asks if her mom got her a Garfield binder too; the girl replies that she got a "geeky" Apollo 11 moon-walk binder. What happens next is incredibly sweet, especially considering that it's Jason.