At one point Mufasa is bemoaning Simba's immaturity and unwillingness to behave. Zazu reassures his king by telling him he actually reminds him of another cub he used to know who turned out just fine, clearly referencing Mufasa himself. It's a reference sure to induce "Awwwww"s all by itself (Cub Mufasa!), it's Zazu doing his job by showing his concern for his king and advising him truly, and it shows for all his irritation and annoyance with Simba, he must believe in him since he's already been through this before with his father, and just compared them favorably. (Not to mention if he's been through it before but is still sticking around, he knows the results will be worth it and it doesn't bother him quite as much as he lets on.)
"They Live In You" and the reprise "He Lives In You." Mufasa sings it to Simba after giving him a lecture about foolishly going to the Pride Lands but forgiving him when Simba understands why his father was so scared; it's about how when Mufasa dies, he will be in the stars watching over Simba, with the great kings of the past. Rafiki sings the reprise as she shows Simba that his father lives in him, and Mufasa appears in the clouds.
Timon forgives Simba for endangering him and nearly causing him to drown in a waterfall. He tells them to stop "talking about dying" and that it's all in the past.
Simba only hugs one person in the show: Rafiki, and she returns it with joy.