Moments pages are spoilers off; beware of unmarked spoilers!
The series in general: in short, a group of friends playing a game together, working towards a common goal, and just screwing around. It's obvious how much fun they have in every series.
Some especially notable examples are when Dean and Mcjones are reunited with the crew after getting lost in an abandoned mineshaft, Jon and Barry's victory over the Ender Dragon, and Paul and Jirard's "trade hug" after defeating Diablo.
Whenever the group takes the time to remember those who have fallen, it usually never fails to warm the heart.
In Minecraft #5 Episode 1note "Ft. Ray Narvaez Jr, Pro Jared, + SpaceHamster!", after PBG opens his inventory for the first time at the end of the episode and the rest of the cast makes fun of him for it, Jared says how much he misses playing Minecraft Hardcore, and the others agree.
Jared: Can I just say I really miss playing Hardcore with you guys?
PBG: Yeah, me too.
Jeff: It is fun.
In Minecraft #5 Episode 15note "BLAZES LEFT AND RIGHT!", during the long battle against the Blazes, while it's not too prominent, PeanutButterGamer can be heard yelling "don't hurt my friends!" at the enemies. It really shows just how much he values them.
Also from Minecraft #5, Episode 20 note "BAD OMEN!!", Jeff's absolutely heart-wrenchingly Big "NO!" when PBG instantly dies from a creeper explosion was uncomfortably too realistic. It's as if he really did lose someone he sincerely cared for, and it makes it all the more saddening.
The final episode of Minecraft #5 has Jeff finding and taming a pack of wolves, calling them his new friends and naming them all Billy. It turns heartbreaking when they all start to die off.
Dean and Lucahjin get along extremely well in Terraria #3, so much so that they form their own team titled: Team New Kids. The attachment even came in when Dean was in charge to pick parties. He immediately picked Lucah without any hesitation, above all other members.
McJones acts as the Babysitter of the group. Surprisingly, he's okay with it when all is said and done!
In Terraria #3, Luke giving a sincere eulogy for Jeff. Since he believed that he was the cause of his death, his tender words mixed with light humor was only appropriate.
PBG's surprisingly sincere attitude towards the allegedly "cursed amethyst hook" that Jeff got himself killed with, going as far as to try and trade his own hook to McJones and take the cursed hook for himself, with the justification that if anyone were to fall to its "curse", no one would be more disposable than himself, in a strangely self-aware, out of character tone. It goes to show just how much PBG understands his and McJones's own values to the group and the importance that the latter has carried throughout the series.
McJones: Who better to handle the cursed item than me?
Near the end of episode 15 of Terraria #3, after defeating the Brain of Cthulhu, PBG needs to take a moment to calm down due to his anxiety spiking. He explains that the tension of Hardcore bosses sets his anxiety off, but as soon as he says he needs to take a moment? Luke is right there with him, calmly telling him to just chill out and breathe.
Luke: You got this man, just take a breath. You are okay. You are okay, dude.
Dean typically watching out for everyone, alerting them when they are low on health in Terraria #3. Some instances include when Lucah was being squished by slush and the entire adventure in the dungeon. Though it becomes absolutely heartbreaking because the dungeon is where Dean dies, warning people about taking damage when he didn't notice his own health.
After Dean dies to spikes, Luke and Reese discuss how Dean was Lucah's new Terraria friend, only to then comment that he wasn't really new. Luke responds with saying that it doesn't matter at all. The end of Team New Kids is easily one of the saddest moments in the season, and is certainly one of the most touching.
In Terraria #3, Luke honoring Jeff and Dean's death by putting the clock that Jeff made for him back in episode 10, and using Dean's Crimson Rod to make a rain cloud above their graves.
Also in episode 23, Lucah saying to Luke "Follow your dreams" after she saves him from drowning. In general, the fact that Lucah calls everyone "friend" can be seen as very heartwarming.
In the finale, Luke dubbing Lucah the "Yo-Yo Queen". She says that she doesn't want a name associated with Yo-Yos as all the Yo-Yo bros but Luke are dead. Luke then points out that he is alive, and Lucah simply says "Well, you're like, the best." D'awwwww.
The alive members saying how far they've come in the finale.
Luke's speech about all the people who thought that Lucah and himself didn't have it in them, and how they managed to get this far.
"Episode 25" of Terraria #3, a post-session podcast where the editor, Todd, and everyone else from the season comes together to discuss their thoughts and feelings on the experience, and Hardcore in general. It's easy to detect the happiness and sincerity in their voices as they reminisce about the whole thing.
The team mentions how floored they were with the sheer amount of fan art that they received over the course of the season, and even showcase several dozen pieces over the course of the podcast.
In Episode 9 of MineZ #2, ProtonToad cheers on McJones from afar after he falls into a chasm and has to claw his way back out.
The final meal of cookies (and an apple) before the group enters the Floating Isles and everyone ends up dead.
Minecraft #6 has the gang finding a Totem of Resurrection, which they can use to bring back one player that died. They eventually choose guest star Dodger, who died just as they brought it back.
Episode 14 of Minecraft #6 has the team vowing to rescue PBG, and later Jeff, when they get stuck in the Nether.
The finale of Minecraft #6 has Jared taking the brunt of the Wither's attacks and dying just before it does, with the team crediting him for the victory and noting if it had targeted everyone they wouldn't have made it.
Starbound HC plays a heartwarming moment for laughs, with Luke meeting his long-lost bird brother in Part 12. He gives him a heartfelt speech, although he almost cracks up at the end.
Luke: Brother... is that you? Brother... Hello. It's me! It's Tweet! All this time, you were here. I can't belie- [the NPC starts walking away] Don't you run. I've been looking for you my whole life, brother! Come back. Please, come back. How is Mom? How is Dad? *starts sob-laughing* I can't believe it...! It's finally you!
In Starbound HC, Lucah ends up being the self-proclaimed mother of the group, since she played the game far more than Terraria. Her interactions with Group 1 is absolutely heartwarming, considering she at some point called the other group members her children.
Because of this, in Part 20 she is unanimously voted to be The Captain of their adventuring party.
The union of the group in episode 9 of Starbound HC is joyous, as this is the first time where Team 1 and Team J are all in one chat, complete with music, Jeff flailing around his spear, and sword dancing. Doubly so since this was completely coincidental, and no one had died at that point.
Minecraft #7 has Jeff and Luke taming two dogs and naming them Billy and Waffle, respectively.
After PBG had a close call in Minecraft #7 and freaked out, his real-world dog Azura charged into the office to make sure he was alright, and as revealed in an off-handed remark, even offered to play fetch with him.
After the episode was uploaded, a Twitter user did ask if PBG did play fetch with Azura after the recording session. He did, by the way, in case you were worried!