At the very beginning, Marco being abandoned by his father, and forced into servitude under the Khan. It really sets the tone for everything to come.
Ling Ling's abuse at the hands of Jia Sidao. When Chabi later learns of it, she's rightly horrified.
Marco's disastrous reunion with his father. Niccolo blows his chance at showing a different side of himself, by attempting to smuggle silkworms out of China, and inadvertently getting his son caught for it. Even still, Marco spares his life, when smuggling silkworms is punishable by death—but Kublai instead has Niccolo and his brother both branded with hot iron to the hand. And he has Marco be the one to do it.
Mei Lin's despair after her failed assassination attempt on Chabi, which she believes will result in her daughter's death.
Marco's sheer dejection and resignation when it looks like he'll be sentenced to death for the failed attack on Xiangyang.
Yusuf incriminating himself in a Heroic Sacrifice to save Marco, since Kublai needs Marco more than him.
Kublai's reaction to Yusuf's "Confession" is especially heartbreaking since this means he would have to not only execute a trusted advisor, but a good friend as well. He fervently denies that Yusuf could ever betray him, knowing it's false, and tells him to play one more chess game with him, only to find that Yusuf took the board away.
Season 2:
Marco's reunion with Kokachin, after the latter has been wedded to Jingim. This is after Kokachin begged Marco to flee Cambulac with her, and he went off to war instead. Now Kokachin has only anger and bitterness for him, masked only by a thin veneer of pleasantry.
Marco: I came for you.
Kokachin:(smiling) And thankfully, I was already gone.
Kublai being goaded by Ahmad into killing Zhao Xian. The boy is terrified by it, Kublai is sickened by himself, and Marco walks in after the fact and is completely stunned.
Hundred Eyes' origin story. He was originally a Wudang monk named Li Jinbao, happily in love with a fellow disciple who went by the name of Lotus. Then the monastery comes under attack by the Khan, and Li is captured, while Lotus is presumed dead. When they meet again, they've been forced to become enemies.
Likewise, Ahmad's origin story. He was taken from his mother when he was a child, and ends up being cared for by Kublai. This is acceptable enough to him, until while exploring the Silk Road, he sleeps with a prostitute... who turns out to be his own mother. He's so horrified by himself that he turns his plans on the Khan from that moment on.
The fate of the stable hand who's the real father of Kokachin's children. Despite everything, Kokachin still makes the effort to visit the grave, and even commiserates with the man's widow.
Ling Ling revealing to her mother that she knows what it means for her mother to have been made to 'dance' for the Khan, and that she's seen a great deal of things while in Cambulac. All that effort to protect her, and it still wasn't enough.
Likewise, Mei Lin leaving her daughter to resume the fight against the Khan. She can't even bring herself to leave while Ling Ling is awake, since that means she'd have to say goodbye.
Khutulun saves Byamba in the heat of the battle, only to realize that Jingim's beaten Orus to death. She's next seen retreating, carrying her brother's battered body over the back of her horse.
Kublai learning of Ahmad's betrayal. To say that he doesn't take it well is a vast understatement.
Kublai telling Chabi of Ahmad's betrayal is also tearjerking as her reaction to it is denial that he would ever do such a thing. The same reaction any mother would have towards her son.
