Babylon 5/Heartwarming

After confronting G'Kar about his intention to smuggle weapons for the Narn resistance through Babylon 5, Garibaldi gives him the name of a trustworthy contact who can handle the smuggling far more effectively, because G'Kar didn't lie to him.

G'Kar: Why are you doing this?
Garibaldi: Because you didn't lie to me.
G'Kar: But you must have known that ahead of time.
Garibaldi: Like you said, I never start a conversation unless I know where it's going... but I always leave a little room for someone to disappoint me. Thanks for not doing it.

When Kosh is being executed by the Shadows for heating up their Cold War, he appears to Sheridan as he sleeps, in the guise of Sheridan's father. Vorlons never do anything without a purpose, and everything they do is on purpose. Think about that- Kosh saw Sheridan as the closest thing he had to a son, and what he did was the only way he could ever show it.
The meeting between "King Arthur" and Delenn, an exquisite symbolism. Two atoners who were similar in personality in some ways and who both knew themselves to have responsibility for the beginning of the Earth-Minbari war, meeting to forgive.
Lennier retaining unshaken his Undying Loyalty toward Delenn after hearing her darkest secret in Atonement:

Lennier: Delenn, I have pledged myself to your side...come fire or storm or darkness or death. Can understanding be a greater danger?

- Most of what Lennier does is either heartwarming or tearjerker. Same goes for every aspect of his relationship with Delenn.
Londo's outright admiration of Vir handling the Drazi spy.
G'Kar was hell-bent and determined to get Na'Toth out of that cell.
"It's easy to find something worth dying for. Do you have anything worth living for?" "Delenn!"
- Let's emphasize this for a minute - John Sheridan loves Delenn enough to defy death. Now that's The Power of Love.
When G'Kar and Londo part ways in Season 5. "Mollari .. understand .. that I can never forgive your people for what they did to my world. My people can never forgive your people. But I .. can forgive .. you."
Londo has had a dream all his life of his death, he would be strangled to death by G'Kar while Londo strangles him. This was taken for years to mean their hatred would kill them both. But as the plot evolves and Londo is given his Keeper, it is shown that it was a tremendous act of love and self-sacrifice. Londo was kept under the control of the keeper for the last 18 years of his life. It would control him and and his actions, using the Magnificent Bastard for evil. 18 years of being a prisoner in his own body. G'Kar, as Londo's greatest foe and friend, releases him from the prison as a mercy kill, despite the Keeper waking up and killing him as well.
- The Expanded Universe takes it one step further. After rebuilding Centauri Prime from the Drakh bombings, Emperor Vir Cotto commissioned two massive statues of Londo and G'Kar, taller than most buildings, to be built to stand like two colossus at the main roads leading to the capital city. They faced outward, at opposite ends of the city but standing back-to-back, as though to defend the capital from harm. Facing in opposite directions, as far apart as could possibly be, but both dedicated to a common cause; you'd have to look far and wide for a more appropriate tribute.
"I'll never leave you, Delenn. Not even if the whole universe stood between us."
The Marriage at the end of Season 4, and G'Kar using his eye to look in and see how it is going...
In a more ironic fashion, in "Soul Mates" when Londo Mollari choses the frankly sharptongued Timov to be his remaining wife. When she asks why, he responds, "Because, with you, my dear, I will always know exactly where I stand." When Mollari leaves her alone, you see her smile a little at her husband's genuinely charming respect for her honesty.
Delenn making it rain.
Any of Londo's Pet the Dog moments, really. One that springs to mind is when he helps two Centauris who wanted to marry for love defy their disapproving families.

Mollari: My shoes are now too tight, and I have forgotten how to dance.
Vir Cotto: I don't understand.
Mollari: Nor should you.
[Later, when he helps the two young Centauri and they ask why]
Mollari: Because you are young, and young people should be allowed to dance!

Later in the series, Londo is part of a Xanatos Gambit that has spun into a Gambit Roulette, with the fate of an entire world in the balance. An assassination attempt has gone awry, and could lead to the death of billions. Londo stands revealed as a traitor, and is helpless to stop the upcoming slaughter... until Vir steps in and finishes the assassination. Londo, realizing this is the first time Vir's ever compromised his morality, tells him that the knowledge that the act was necessary doesn't make up for him, but gently reminds Vir that the overwhelming guilt he feels means he's still a good person. The heartwarming really steps in, however, at Fridge Brilliance: by this point in the story, Londo's killed far better people for far less, with far fewer moral qualms than Vir. Londo has long since convinced himself that he is past redemption, but in a quiet moment where Vir is all but asking Londo to tell him the ends completely justify the means, Londo caringly but firmly tells him that they don't, because he knows better and wants what's best for Vir.
The end of the Vorlon/Shadow War in Season 4, after Sheridan and Delenn tell them both off, Lorien steps forward and explains that they need to let go of the younger races, leave the galaxy to them, and move on as he and his kind did long ago. The Shadow is the first to respond, in such an unexpectedly innocent tone. The Vorlon's response is much the same. They were simply afraid, and Lorien's reassurance of them is equally as heartwarming.

Shadow: Will you... come with us?
Lorien: I have been here since the beginning. I will not leave you now. I will go with you beyond the Rim, and we will see again all those who went ahead of us. All those who we have missed for so long.
Vorlon: Then we will not be alone?
Lorien: No, never alone.

The Grand Finale is made of heartwarming. While Babylon 5 dies in fire, the light does not go out. It taught us many things, but mostly there is still hope, even for people like us.
The penultimate episode has a very moving Call Back to the Season 1 credits, where all the main characters lined up in front of the window in C&C. Only now, all the characters are the replacements, stepping up to take the place of those who've moved on: Captain Lochley replacing Sinclair/Sheridan, Lt. Corwin replacing Ivanova, Number Two replacing Lyta, Zack replacing Garibaldi, Lillian Hobbs replacing Dr. Franklin, Ta'Lon replacing G'Kar, and Vir Cotto replacing Londo. It's an incredibly poignant Passing the Torch moment, showing that no matter what happens, Babylon 5 will still be there.
- Even more heartwarming than that, the Grand Finale also features A Creator Cameo of the entire production crew, along with a shoutout to "Those of you who have been archiving this Special ISN Documentary...
Lennier sticking his neck out for Sheridan in a big way in "There All the Honor Lies", despite having had family on the Black Star.
Neroon finally working together with Delenn.

Neroon: Dukhat chose you above all to follow him. Slowly, dimly, I begin to understand why. I do not know what lies ahead of us, Delenn. But I do know that it is right that we are here together.
Delenn: Was that a compliment, Neroon?
Neroon: [Actually smiling] After a fashion.

The station holds a festival for each race to demonstrate their most prominent religious rites. Sinclair is tasked with providing humanity's demonstration, and naturally is overwhelmed at how to do it when we have so many different religions. In the final scene, he gives his demonstration, introducing the other ambassadors to a member of each of humanity's religions, enough that they fill an entire hallway, making the point that what truly makes humanity's religion special is the ability for so many different kinds of belief to exist in harmony. There are reports of crew members having Manly Tears as it was shot.
All of Sheridan and Ivanova's relationship. Their friendship was one of the mainstays of the show's entire run, and proved that a relationship didn't have to be romantic to be heartwarming, awww-worthy, and generally all-around awesome.
- Ivanova's last request was that Sheridan win the war from the bridge of the Agamemnon. So he did.
Lochley sending for Lise to help Garibaldi out of his funk at the end of season 5.
In Passing Through Gethsemane, when Brad Dourif's character (Brother Edward) tells Delenn what the defining moment of his faith is. He describes the scene in The Bible where Jesus prays in the garden at Gethsemane for his terrible fate to be passed on to someone else, and how he eventually found the strength in himself to let the Roman soldiers capture and imprison him. Dourif does an incredible job of delivering the monologue, and it's no wonder Delenn looks like she's on the verge of tears as she listens to him. What makes this doubly awesome is that the scene was written by an atheist.
- Also, the final scene of the episode, where Brother Theo shows that he has found it in himself to forgive the man who murdered Brother Edward, and convinces Sheridan to do the same, with nothing more than softly-spoken words.