The first is undoubtly when Tamahome tries to kill Miaka after he takes a brainwashing potion and her trying to commit suicide over it all. Luckily Hotohori is on hand to save her and make her feel better, untill the spell over Tamahome is broken.
The second is when Tamahome's family is killed by Suboshi
Another is when Nuriko was killed by Ashitare. He was the first big, loved character to die and anyone who didn't at least have watery eyes must have a heart of stone.
Also, the death of Hotohori, who was killed by the main villain of the series, Nakago. He also left behind his pregnant wife, Houki - who closely resembles Nuriko.
Also the deaths of Chiriko and Mitsukake, who both had major parts on the 'good' team. It is also debated whether Tamahome died and came back with the others, or whether he just didn't die, full stop.
One moment was when Tamahome saw into Nakago's heart, just before Nakago died. After his tribe was destroyed - and he killed his mother by accident with his new-found powers - he was captured to be a toy for the Emperor. His best friend, Tarlia, had also been captured and was executed right in front of him to try and bribe him into using his powers to save her. He does use his powers, but he was too late to save her. Years later, when fighting for control of the Kutoh army, he kills the man in charge - seconds before realising that the man he had killed was his father.
The episode where we learn that the reason for Yui's Face–Heel Turn is due to the fact that she got raped upon entering the book alone. She wasn't really, she fainted and Nakago killed the men who tried to rape her before anything could happen.
And on the same length, the episode where Miaka chooses to face Nakago and get the Shinzaho back from him, ending up with her being raped. Again, she is not raped. She lost consciousness and her status as Suzaku no Miko kept Nakago from doing anything