Red Dwarf/Heartwarming

In the episode "Waiting for God", Lister -- who has discovered that the race of Cat-people who evolved from his pet cat worshipped him as their God 'Cloister the Stupid', has discovered a dying, blind cat-priest who has lost his faith and succumbed to bitterness. Making a grand entrance as Cloister, Lister ensures that the man goes to his grave happy that his God has finally validated his faith:

Priest: [Despairing] You tested me, Cloister, and I failed...
Lister: No, you didn't fail, old man. You passed. I'm giving you an A-plus Distinction.
Priest: You mean... there's a place for me on Fuchal?
Lister: A place? You got your own bathroom ensuite. Corked floors. Your own barbeque on the patio, double-glazing. A phone, everything.

Beyond a Joke, when Kryten realises that he's been able to make something of himself and do so even though his jilted creator had invented him as a Take That at her ex.
In Holoship, when Rimmer lists all the reasons he considers himself a failure, but Lister actually tells him there was nothing wrong with his job or the way he lived his life.
In Thanks for the Memories, the crew celebrate Rimmer's deathday. Afterwards, a drunken Rimmer tells Lister that he only ever made love once in his entire life. Lister decides to fix things, and adjusts Rimmer's hologrammatic memory...

Rimmer: You gave me eight months of your life... as a present?

Stoke me a Clipper. There are quite a few little moments in this one, but to my mind the best is at the end, when the crew are having a funeral for "Rimmer" (actually Ace) and Lister awards him a posthumous First Officership. Then all the crew perform a Rimmer-salute.
- Even better, when Rimmer leaves, he shakes hands with Kryten and Cat. But he and Lister hug.
In the episode where Kryten is to be replaced by the latest android model Hudzen 10, the crew, hungover as they are, vow to fight to protect Kryten. Even the normally selfish Cat. Kryten muses if this is the human quality called "Friendship". Lister says "It's too early in the morning for that Star Trek crap!"
- Also Kryten's entire "night to remember," if only because it's one of the rare times when all the Dwarfers are working toward one goal without bickering, something that's usually damn near impossible, in order to give Kryten a decent farewell.