Caesar: Lucky for us I got my foot-to-behind boots on!
Uncle Ruckus' brothers, Darryl and Darrell helping Ruckus dig their grandmother's grave. This is especially heartwarming as it shows that despite Ruckus' terrible upbringing, his brothers and his mother are still nice and respectful to him. And despite his racism and... everything else about him, he's still proud of his black mother and brothers.
Really, any episode focused on Ruckus is going to have at least one Tear Jerker and one of these.
The episode "The Story of Jimmy Rebel", in which Uncle Ruckus (a self-hating black) befriends a racist white man and ends up converting him after seeing how other racists treat him.
Jimmy Rebel: You remember when I said we hate the blacks because of their attitudes?
Uncle Ruckus: Yeah.
Jimmy Rebel: Well, I think that's a load of shit. You're just one of us, Ruckus, but they still hate you. And it's not your attitude. It's 'cause you're black. [...] I've made some of the best music of my life with you, Ruckus, and I don't intend to stop.
Uncle Ruckus: Well, if we ain't gonna be singin' 'bout no niggers, what are we gon' be singin' about?
Jimmy Rebel: There's so many other things to make music about! There's friends, and good times, beer, love, all kinds a' shit!
From the strip: Huey has heard a friend back home died and is driven to tears:
Huey: Why couldn't life be like Star Wars, where your loved ones can just come back as blue ghosts?
Caesar: Well, we'd have Ewoks and Jar Jar running around. Nobody wants that.
Huey: A small price to pay if you could have your loved ones come back as blue ghosts.
The ending of "Riley wuz Here". He spraypainted a large portrait of his parents at their wedding onto the house. Even Granddad cried!
Jazmine and Huey at the end of Wingmen. As well as Granddad putting the "Deez Nutz" jar his friend left him in his will up on the shelf with other pieces of his past.
Huey: Your pain is the breaking of the shell that encloses your understanding. It is the bitter potion by which the physician within you heals your sick-self. Therefore trust the physician, and drink his remedy in silence & tranquility, Khalil Gibran.
The ending of "The Trial of R. Kelly". After Tom is humiliated in court, Sarah and Jazmine are there to comfort him and remind him he's not such a loser.
In "The Passion of Reverend Ruckus" Huey goes to extreme lengths just to save one person from death row, only to be thwarted by his own situation and Granddad's apathy. Huey begins to cry and pray for some sort of divine intervention. This is especially poignant since it's the one and only time we see Huey cry and, up to that point, he has been portrayed as an atheist. Even through his hard, mature exterior, Huey is still a kid and never is that clearer than this moment.
Huey: I've never prayed before. I don't even know who I'm praying to. I may be too young to know what the world is supposed to be, but it's not supposed to be this. It can't be this. So please...
Also, earlier when Huey protests to Granddad to help him breakout a Death Row prisoner, but he decides to go Ruckus' televangelism event. It turns out that Granddad couldn't help Huey only because he wanted to stop Ruckus and talk some sense into him. Despite everything that Ruckus is, and stands for, Granddad still saw it as his responsibility to help him:
Huey: But Granddad, you promised to take me into the prison tonight!
Granddad: Not tonight - someone has to talk some sense into Ruckus.
Huey: But I'm trying to save my friend!
Granddad: Me too.
Huey's actions in "The Block is Hot". He spends the entire episode trying to stop Ed Wuncler Sr. from taking advantage of Jazmine, then at the end underscores it by handing Jazmine his scarf once it starts snowing. The same one he's been wearing through the whole 90 degree heat wave. The kid might have some Jerkass tendencies, but let no-one say he doesn't care about his friends.
Also from "The Block is Hot." It's pretty minor, but when Jazmine snaps at him and tells him to go away, Huey actually seems genuinely sad. Despite his personality, he's still a 10 year-old boy who gets hurt when his friends get mad at him.
After three seasons of pretty much ignoring, mocking, and disrespecting him, in "It's Goin' Down", Grandad and Riley both hug Huey, say how worried they were for him, and then say how proud they were of him. Granddad even says he should have listened to Huey more often, and says he will.
Granddad accepting Riley as gay at the end of "The Story Of Gangstalicious Part II". He wasn't, but still.
The end of the episode about Lando.
The ending of the relationship of Granddad and Ebony Brown. A breakup with good character development.
Huey and Granddad's exchange and the end of "The Hunger Strike"
Huey: Granddad, What do you do when you can't do nothing, but there's nothing you can do?
Granddad: You do what you can.
The ending to the first Stinkmeaner episode. Huey's narration mentions just what a shitty human being Stinkmeaner was, and how the world is probably better off without him. But, in Huey's own words: "Still, he was our brother". Cut to Robert and the kids having a small funeral service for Stinkmeaner. Regardless of Stinkmeaners eventual release from hell, this was a very touching moment.