The ending of the series is pretty heartwarming. Sure, all the characters go their separate ways, but they promise to see each other again (which they do in the bonus chapter) and in the end, everybody is happy. The best part is seeing that Kenshin and Kaoru at least are now Happily Married and have a son.
It's a darker moment, but Hoji reuniting with Shishio and Yumi in hell. He's just so happy.
A small one for Saitou. He has an undercover persona as a medicine peddler from Tama who specialises in a medicine called Ishida Sanyaku. For those who don't know, Hijikata Toshizou was from Tama, and he went around selling Ishida Sanyaku prior to becoming the Vice-Commander of the Shinsengumi. It's a subtle way of Saitou remembering his deceased friend.
Misao and the rest of the Oniwabanshu meet Sano and believe him to be some street thug. Kenshin smiles and says that there is no one in the world that he trusts more than Sano.
The scene where Hiko meets Young Kenshin for the first time is this way.
"I have a found a pupil, consider yourself fortunate..."
Haanya looking after Misao even from the afterlife.
Live Action Film
Kaoru shattering Jin-e's lethally strong Shin no Ippo technique which froze her lungs through her sheer love for Kenshin to stop him from becoming a murderer again to save her life:
Kaoru: "KENSHIN DON'T!! Don't become a manslayer again... Please don't kill him... Kenshin... For those who died by your blade... And for everyone whose life... you have saved.... Please don't kill him... A sword that doesn't kill.... A sword that can protect.... For this new age.... of peace... Isn't that what you fought for?"
Equally so back in the original manga/anime.
The ending surely deserves a spot here. After Kaoru is rescued by Kenshin, she wakes in the dojo with a start. She then looks around, finding Sano asleep in the adjacent room, while Megumi and Yahiko are in the kitchen, but Kenshin is nowhere to be seen. Panicking, she assumes he's left the dojo to wander once more and rushes towards the gate (not bothering to put on her sandals to boot). But she stops when Kenshin appears at the gate with the day's groceries. And when Megumi (who gently admonishes Kaoru for jumping to conclusions), Yahiko and Sano join them, the following exchange occurs:
Hiko Seijuro's whole relationship with Kenshin is this. This movie shows much more than the manga Hiko's role as a Parental Substitute to Kenshin, from the fact that he doesn't abuse (too much) the "baka deshi" nickname, to the fact that during the "will to live" test, he had several chances to deal a death blow to Kenshin but always left him enough time to recover (even if it's more than likely that manga Hiko was reluctant to deal a deadly Kuzu Ryu Sen to Kenshin), to his behaving outright fatherly after teaching him Amakakeru Ryu no Hirameki. Even Hiko's trademark arrogance towards the Rurouni has almost completely disappeared, only appearing at the beginning, and it mostly looks like retribution for Kenshin leaving him 14 years ago.
Hiko "Don't die."
Misao telling Kenshin that Kaoru is still alive
The ending, with Kenshin saying that he would like to watch the new era with Kaoru in the Kamiya dojo.