In episode 6 "Tetsusaiga: the Phantom Sword", when Sesshomaru attacks Inyuasha once he'd learned the location of the Tessaiga, Sesshomaru killed the demon who had impersonated Inuyasha's mother upon his orders but had a HeelFace Turn due to her coming to think of Inuyasha as her child per her motherly instincts. No wonder Kagome was pissed at that.
The episode "The Soul Piper and the Mischievous Little Soul", with Mayu the angry ghost girl, whom Kagome helped to go to Heaven instead of being devoured by the flames of Hell ("Kagome-san... you think my Mama is still angry with me?" "No, she's not... she's still your sweet and gentle Mama, after all!").
There's the scene where Kagome had yet another argument with Inuyasha and then watched a rather intimate scene with him and Kikyo that made her come back home for several days. Eventually she falls to her knees in front of the tree in the Higurashi shrine, cries and realizes that she loves Inuyasha. In the anime, there's even a scene added of Kagome's mother telling a story, where she tells how she and Kagome's father declared their mutual love in front of the same tree, which also happens to be the tree Inuyasha was pinned to with Kikyo's arrow, which definitely does not help.
Band Of Seven
Add Jakotsu's last moments, right in between his defeat to Inuyasha and Renkotsu killing him. He resigns himself to die but is happy anyway, because his second life might be over but he lived it at its fullest and had no regrets,
It's just a small line, but it's tearjerking to hear a smug snake like Renkotsu tell Jakotsu to forgive him right before he removes the shard, especially since he's the one that set up Jakotsu to be slaughtered by Inuyasha. There's no one around (or so he thinks), he just feels that he has to ask for Jakotsu's forgiveness. And when he does, he replies with nothing but a smile, basically saying "I know what you're doing, but it's ok."
What makes it worse is at the beginning (or maybe the episode before it) Jakotsu and Bankotsu met for the last time. Bankotsu told Jakotsu that he was his only real friend, the only person he could really trust. *sniff*
Ginkotsu's death in the anime, as he gives his life to save Renkotsu, his only friend, to stop Koga via Heroic Sacrifice
Bankotsu's death, Inuyasha viewed as a Worthy Opponent and is angered when Naraku insults his honor to his comrades.
Sango loses her family and village in the span of a day or two.
After Kohaku wounds Kagome and takes the shikon jewel fragments from her, Sango concludes that her brother is still under Narakus control. She crosses the Despair Event Horizon and makes the decision to kill him, then follow him in death by committing suicide. In a Heartwarming Moment, Inuyasha stops her just in time and explains that Kohaku could have killed Kagome but didnt.
The last few minutes of "Sango, Kohaku, and a Secret Garden." Kohaku and Sango's near-miss tugs on the heartstrings enough on its own, but Sango's return at the end of the episode, set to a swelling orchestral version of her musical theme, makes it a Tear Jerker.
The death of Kagura in "Wind," possibly the most beautiful and certainly the most poignant chapter of the manga to date, almost topping even Kikyo's death later in the series thanks to the very effective layout of the pages.
Specially when right before before this, when Inuyasha and co have realized Kagura's change of heart and how she just wishes to be free of Naraku, Kagome asks her if she wants to join up with them. Upon rejecting the idea, Inuyasha tells Kagura they'll retrieve her heart from Naraku, so "don't you die, okay?" Kagura then runs into Naraku a few moments later, who returns her heart only to impale her torso and fatally poison her with his miasma.
And especially when it becomes clear that Sesshomaru had almost reached Naraku's heart when he scented Kagura's blood - Jaken's downright baffled when Sesshoumaru suddenly speeds off in the wrong direction. For the first time in the manga, he gives up something he personally wants (Naraku's death) for someone else... only to discover that he cannot save her with Tenseiga, after all. All he can do is stay with her until she dies so that's exactly what he does, which allows her to die happy because the last thing she ever wanted to see before she died was Sesshomaru.
Kanna's death is also very sad, even more so in anime in which she'd finally found her emotions and her heart and knew what they were, and seemed satisfied with that.
Kanna's demise tugged my heart strings and would not let go. The entire gang calling for her not to give her life up for Naraku made it all worse...
The ending. Chap. 557: "I'm... not going to wish for anything. Inuyasha will come...! I believe in him!" In particular, pages 15 and 16
One of the chapters near the very end, whilst most of the gang are Fantastic Voyage-ing inside Naraku's giant spider body, has Sango and Miroku completely giving up all hope, and lying down together to eventually be killed together by Miroku's Kazaana/Wind-Tunnel/Air-Rip.
In the anime, a mind-wiped Kohaku believed that Sango (who he didn't recognize or remember) had been killed - 'She's dead then, that woman...' - and starts crying without even knowing why.
After Mukotsu poisons Miroku, Sango, and Kagome. Shippo does his goddamned best to try to help them but can't seem to do anything. The pure look of helplessness on his face knowing he can't save his friends is heart-wrenching.
Oddly, Manten's death, at least in the animé episode "Phantom Showdown: The Thunder Brothers vs. Tetsusaiga". Yes, he and his brother, Hiten, were a couple of jerks who did a lot of terrible things, including killing Shippo's dad and trying to kill the heroes, but it's really depressing to watch when Manten, after spending his entire life trying to get a head full of hair and failing, is wishing to be reincarnated as a bald guy again just so long as he's reincarnated as Hiten's brother.
Sara from episode 134 "The woman who loved Sesshomaru" is a really tragic case. But she seemed happy before she passed on at the end of the episode, so it might be more like a Heartwarming Moment.
Though only in the anime for a single episode, Ayame manages to draw a tear when Koga finally remembers her. Koga's last line in the episode hits hardest, since he has spent the entire episode denying that he remembers her.
Koga: I have no intention of losing to Naraku. Once I get my revenge, there's no assurance I'll be alive. Forget about the moon and the rainbow, Ayame.
And of all tear-jerkers, Kikyo's death. It's really too much for a woman to try to be strong and stoic when she was still alive, for her village.
Kikyo: I must show my weaknesses to no one. I must never have doubts or demons would overtake me. I am human yet I cannot be human. We are quite alike you and I. You half-demon...That is why I could not kill you.
Then Naraku just decided to screw up Inuyasha and Kikyo's almost happy life by fooling both, and Kikyo dies with a broken heart and a grudge that would reside for centuries in Kagome's soul.
When she should have been given at least a peaceful after life, a demon witch just decides to resurrect her, as a clay body that can no longer feel. Adding to that, the soul she got from Kagome was full of bitterness and anguish at Inuyasha's supposed 'betrayal'.
Kikyo: To live is to die. To die is to live. My name is Kikyo. I am a priestess who is unable to leave this world and reach the sacred place. No, that is not entirely the truth. Once I was a priestess. Now I am but a corpse with a cursed, false existence. No matter how much I desire to do good and help others, the truth is I live off the souls of the dead.
When she finally dies, her lines to Inuyasha are... so melancholic yet bittersweet. (the orchestral version of Dearest only makes this even more heart wrenching)
Kikyo: I wanted to live as a normal woman with you, Inuyasha... and now I die a normal woman, without the Shikon, in your arms.
The English dub of Kikyo's death is especially powerful, with Richard Ian Cox completely selling Inuyasha's tearful breakdown.
There was this filler mini-arc (episodes 137 to 140) about a male youkai named Hoshiyomi and his dead girlfriend, the human Magical Girl Warrior Tsukiyomi who died many years ago, and whom Hoshiyomi hates because he mistakenly thinks she betrayed him. Not only there are parallels to Inuyasha and Kikyou, but it's a tear jerker from the start to the end. Especially the end, when Tsukiyomi manages to speak to Hoshiyomi through Kagome's body, but he's still too embittered so Kagome and Inuyasha have to finish him together.
Even more so his heel realization as he dies and states (in the dub), "This is for the best, right Tsukiyomi?"
Inuyasha's explanation of what it means to be a half-demon.
Inuyasha: "But that's what it means to be different. No one trusts you. You're always the first to be blamed. And it is always, ALWAYS, your fault!"
The part late in the series when Sango is forced to dissolve her Hiraikotsu with poison to kill the chapter's villain and save Miroku. Later she's given the chance to restore her weapon by an old master of poisons, who lets her go into a magical jug to "slay the youkai inside". Once she's there, Sango eventually realizes the youkai she's seeing are the spirits of the youkai that were used to make Hiraikotsu, and they're all mad and hurt, asking her why she betrayed them. Sango has to convince them to become Hiraikotsu again, to which they say they'll do so only if she promises to never betray them again. She can't promise it however as Sango knows if it comes to choosing between destroying Hiraikotsu or saving Miroku again, she will choose Miroku. While this is happening, Miroku is drinking a poison that will free him from pain so he can keep using his Wind Tunnel and protect Sango, even though a wound inside his body is getting closer to killing him everytime he uses it. The youkai with Sango are able to sense this, and when they realize the great love between her and Miroku, they agree to return to being Hiraikotsu and fight by her side once more.
After Naraku is defeated, Kagome returns to her time period and the well ceases to work. Even three years later, she thought about Inuyasha every day.
The well works (probably as a one way trip) and her mother encourages her to follow her heart, even though she knows they will probably never see each other again.
"I am the wind... the free... wind."
"Kikyou said that she'll protect us....forever."
"Houshi-sama... please... take me with you."
Ane-ue... what have I done... ANE-UE, WHAT HAVE I DONE?!"
"Please remember me Lord Sesshomaru.... even if I die."
"The light....will be the thing that destroys Naraku."