When Elder Haman is marking all the waygates for Rand and begins crying on the map for all of the Ogier-built cities and groves lost.
Aram's death in Knife of Dreams.
Verin's death in The Gathering Storm.
Aviendha's vision of the future Aiel in Towers of Midnight. A supremely epic vision of the degradation and fall of your honorable people, all fated to happen and caused by your descendents. The reader cannot help but feel for her and weep.
"Yes, Rand al'Thor." She suddenly sounded hoarse. For a moment she turned her face away, eyes shut and quivering. "I hate you with all of my heart. I do. And I always will."
This doesn't sound like much until you remember what Aviendha is feeling. She is in love with him, but her BFF Elayne also loves him, and she promised Elayne she would safeguard him from the claws of other women. Now she is the other woman. Poor thing probably hates herself—and that's before we factor in the whole Proud Warrior Race thing.
The funeral in Towers of Midnight. Faile and her retainers coming together one night to remember the Mera'din Aiel who watched over and protected each of them in Malden, ultimately at the cost of their own lives.
A Memory of Light, the deaths of a good chunk of the main cast, including Siuan, Gawyn, and Egwene, along with plenty of lesser named characters.
The moment when Logain gives up searching for the other male sa'angreal in order to help save the refugees from Caemlyn and their children from the Shadowspawn, and thus fulfills Min's viewing of "glory of men to come":
He had abandoned that power for what? To save these refugees? People who would spurn him and hate him for what he was. People who...
... who looked at him with awe.
Logain watched with wonder as the people flocked around his Asha'man,weeping for their salvation. Elderly men took Asha'man by the hands, overcome, praising them.
Nearby, a youth looked at Logain with admiration. A dozen youths. Light, a hundred. Not a hint of fear in their eyes.
"Thank you," the young mother said again. "Thank you."
"The Black Tower protects," Logain heard himself say. "Always."
"I will send him to you to be tested when he is of age," the woman promised, holding her son. "I would have him join you, if he has the talent."
HERE IS THE TRUTH, SHAI'TAN. YOU CANNOT WIN UNLESS WE GIVE UP. THAT'S IT, ISN'T IT? THIS FIGHT ISN'T ABOUT A VICTORY IN BATTLE. TAKING ME... IT WAS NEVER ABOUT BEATING ME. IT WAS ABOUT BREAKING ME. THAT'S WHAT YOU'VE TRIED TO DO WITH ALL OF US. IT'S WHY AT TIMES YOU TRIED TO HAVE US KILLED, WHILE OTHER TIMES YOU DIDN'T SEEM TO CARE. YOU WIN WHEN YOU BREAK US. BUT YOU HAVEN'T. YOU CAN'T.
Oddly enough, Lanfear is the subject of a couple of these. Her confrontation with Rand in his dreamshard, where he reveals to her he does not love her and never did, is rather heartbreaking, and she almost, almost relents, allowing him into her mind and coming this close to coming back to the Light. In the end even Rand pities her for not knowing love and in fact being incapable of ever feeling it because of her need for power. Then near the very end when she once again falls her into The Starscream pattern and attempts to get Perrin to kill Moiraine, so she can kill Nynaeve, claim Callandor, and use Moridin's power to make Rand kneel while saving the Dark One from him and thus earning the greatest power she can possess, Perrin is forced to kill her. She had gone so mad from isolation, loss of love, pride, and desire to rule that she had to be put out of her misery... but it's still quite tragic. It's also an in-universe example since Perrin, still under Compulsion to love her, cries over her body.
Each time one of the Great Captains realize they have betrayed the light due to Compulsion is rather heartbreaking. These are good and great men who serve the light willingly and are prepared to die for Rand and the world, and then they realize that they have been forced to betray their men and their oaths. Each one is different but when they realize they sent good men who trusted them to die is terrible.
"Suddenly, Olver felt a deep warmth. He had lost so many people, but one of them... one... had come back for him."
Gawyn's last words.
Gawyn: You won't be [left without a brother]. You have another brother, Galad. One you do not know. A son of... Tigraine... who went into the Waste... Son of a Maiden. Born on Dragonmount... Don't hate him, Galad. I always hated him, but I stopped. I... stopped...
The history of the Aiel revealed in The Shadow Rising certainly counts. It takes up chapters 25 and 26 of the book, and it is heartbreaking.
In The Shadow Rising it was heartbreaking reading Perrin's reaction to finding out that his family is dead, especially with everything that he risked to get to them quickly.