Jason's most cherished memory? Coming down with the Flu as a child and, after being told he can't come on patrol, having Batman surprise him and spending a night in together.
Jason spending time with Tim, who completely forgives him for everything he did to hurt Tim.
The Flashback in Issue 6, between Jason and Kory where she lends him the sympathetic and non-judgmental ear he's needed for so long and convinces him to finally move on from his past and let go of his anger. Complete with a genuinely affectionate hug.
Jason taking the time to say good-bye to Damian, Dick, Alfred and Bruce after Death of the Family, even telling Damian that he can always talk to him or one of the other Robins if he feels like no one gets where he's coming from. Also, Roy's and Kori's delight at seeing Jason again.
Blackfire and Starfire's reconciliation in the "Origin of Starfire arc." Blackfire's tearful apology to her sister, Starfire forgives her right away.
Pretty much all of issue 18. But the crowning moment though would be when Jason and Bruce hug each other tight at the end after Jason wakes up from his coma.
It also shows a flash-forward of :Jason, as Wingman for Batman Incorporated apologizing to Bruce for not doing more to save Damian from ultimately being murdered. And also goes into further Tear Jerker territory as, with his amicable relationship with Damian as mentioned above, sees Jason dealing with the guilt that Damian was murdered by his own clone indirectly because of Talia, who Jason feels he owes so much to.
Arsenal's recovery from alcoholism. At his lowest point he attacked Killer Croc in a suicide attempt. When Croc realized this, rather than trying to kill Arsenal he stopped the fight and told Arsenal to get some help. This inspired Roy to quit the booze and it's later shown that Croc even became his sponsor, implying the two have struck up a friendship. It's a heartwarming moment for both Roy (overcoming his addiction) and Croc (actually getting a friend; any long-time comic fan can tell you that Killer Croc could reallyuse a damn hug).
Despite Croc haven't seen at all outside of flashbacks, He's still a really important person for him, so important, that the rumor of someone fitting Croc's description having problems with the mafia on Hong Kong was enough for Roy to go at his help; ditching Jason and Kory in the process.
Anytime the Outlaws show that they legitimately care for one another is this.
Blackfire tries to help Starfire recover from her drug addiction.
DC Rebirth series:
Jason kept the tire he stole off the Batmobile and his "graduation" photo, which captured in eternity the image of Batman smiling.
Jason using what he remembered of his therapy sessions in Arkham to calm down and take care of the "newborn" Bizarro instead of fighting him. Ironically enough, his therapist was none other than Harleen Quinzel herself, showing that opposite to the Joker, she had a positive impact on Jason's life, which is especially poignant.
Jason being unable to kill Bizarro and opting to keep him around, trusting the somewhat mindless brute.
Quite a few warm and fuzzies all throughout Annual #1. From Jason bringing Dick in only partially to assist with a case involving a circus (and mostly to spend time with him), to their relationship as adoptive brothers being established more firmly and explicitly than it ever has been in canon, to Dick casually referring to Bruce a couple of times as "father", to Bizarro's pure and budding romance with a bearded woman, this short issue delivered many happy feels, both big and small.
Annual #2 continues the trend by rekindling Jason and Roy's friendship, with Jason finally being able to openly admit to Roy's face that he is his best friend. Unfortunately it becomes a Tear Jerker with Roy's death in Heroes in Crisis
Roy is still in contact with Croc and we see they are still good friends. Waylon even encourages Roy to go back into rehab. They finish the call by holographically touching hands, despite Croc's guards warning him to not move.
After the brutal fight between Batman and Red hood, Bruce went out of his way to look for Jason to break the news of Roy's death. While the two are still on bad terms, its heartwarming to see Bruce acting like a father figure to his grieving son and even offering him a ride.
In continuation of Red Hood/Arsenal, Jason offers the Su sisters a more legitimate means of earning money by acting as his staff. And just before leaving Gotham, Jason gives Suzie ownership of the Iceburg Lounge to help her out.
Issue #30 confirms that Kate Kane and Renee Montoya are still a couple after they began to rekindle things in the final issue of Batwoman (Rebirth) months earlier.
After Jason gets tasked in teaching kids how to use their powers for evil, he decided to take the other way round and stealthily teaches them the value of teamwork. In Chapter #41, it's even shown that he took them all to Ma Gunn's orphanage with him promising not to give up on them.
