She had many suitors. One of these was the god Apollo. Apollo promised to teach Cassandra the gift of Prophecy in exchange for sexual favours. Cassandra accepted the conditions but once she had the gift she denied Apollo his prize. In revenge, as he could not take back the gift, Apollo made it into a curse. Cassandra would only be able to see and tell the truth of her prophecies but no one would ever believe her.
Because of this Cassandra was thought mad and was often locked away. This happened when Cassandra was the only one to recognize the shepherd Paris as her long lost brother Alexandros. It was not until King Priam admitted who Paris was that he was welcomed home.
Another of Cassandra's prophecies was that if Paris went to Sparta it would only bring trouble for Troy. This too was correct as on Paris' return with the now renamed Helen of Troy, Cassandra again had to be locked up after seeing Troy burn as a result (the Trojan War).
Another of Cassandra's suitors was Othryoneus from Cabesus, a sojourner who had been promised the hand of the beautiful Cassandra if he helped Troy to beat the Greeks. Unfortunately Othryoneus was killed by Idomeneus during the war.
At the end of the war Cassandra predicted that Troy would fall at the hands of an army hidden in the belly of a wooden horse. Again she wasn't believed and when the Trojans saw the wooden horse in the field as an offering by the Greeks, they decided to take it inside the walls of Troy to the temple of Athene. From here the Greeks hidden inside were able to let in their comrades and massacre the Trojans.
When the massacre started Cassandra fled to the temple of Athene where she wrapped herself around Athene's statue and prayed for sanctuary. While she was the Locrian Ajax (the Lesser) came across her. He dragged her away from the statue by her hair and then proceeded to rape Cassandra. Ajax then gave Cassandra to Agamemnon as a war prize.
In revenge for the desecration of her temple, Athena enlisted the help of her father Zeus and her uncle Poseidon in ensuring the Greeks did not return home (they did not punish Ajax for the desecration so all would be punished). She was especially cruel in the demise of Ajax the Lesser.
Before they could return to Mycenae Cassandra, by now Agamemnon's sex slave, bore him twin sons - Teledamus and Pelops. On Agamemnon's return trip Cassandra prophecied that the four of them would be killed. Unable to convince Agamemnon and knowing it was her fate, Cassandra knowingly sailed on to her death.
On their arrival at the palace at Mycenae, Agamemnon and Cassandra were killed (possibly by stabbing) by Agamemnon's wife Clytemnestra, while the twins were killed by her lover Aegisthus.