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.
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.
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.
Jason being unable to kill Bizarro and opting to keep him around, trusting the somewhat mindless brute.