Agamemnon
Agamemnon was one of the sons of Atreus. He and his brother Menelaus were banished from Mycenae after their father was killed by Aegisthus and Thyestes took the throne.
Helen of Troy
Menelaus sought the hand of Helen, who was the most beautiful woman in the world, as well as immortal (her true father was Zeus in the form of a swan). A number of other suitors sought her hand, and to prevent open warfare from breaking out, her mortal father required them all to agree to defend the winning suitor, and then had them draw straws. Menelaus won the draw and married Helen while Agamemnon married her mortal half-sister, Clytemnestra.
The two brothers thereafter returned to Mycenae and drove Thyestes away. The brothers got along remarkably well, especially considering that they belonged to the House of Atreus, and they apparently amicably agreed that Agamemnon would be king of Mycenae while Menelaus became king of Sparta after Helen's mortal father died without male heirs.
Unfortunately, Aphrodite, the Goddess of Love, had promised Paris the hand of the most beautiful woman in the world, as a result of the Judgment of Paris. While Menelaus was away, Aphrodite induced Helen to run away to Troy with Paris, precipitating the Trojan War.
Iphigenia
Agamemnon took the lead in raising the troops to go to war, including collecting the fabled "thousand ships". Once the ships were collected at the port of Aulis, however, the fleet was unable to set sail for many days due to adverse winds. Eventually Agamemnon swore to the gods that, in order to make the weather improve, he would sacrifice the first living creature that greeted him when he went home.
Agamemnon duly went home, but instead of the dog (or possibly slave) that he expected to greet him, his beloved daughter Iphigenia ran out to meet him. Oaths to the gods were very serious business, so Agamemnon decided to proceed with the sacrifice. Returning to Aulis, he sent for Iphigenia under the pretext of marrying her off. He evidently feared what Clytemnestra might do if she knew of his plans, and rightly so, as Clytemnestra seems to have been well-suited to the House of Atreus.
Agamemnon was prepared to sacrifice Iphigenia, but Artemis intervened and whisked her away to be a priestess in Tauris. The attempt was enough, though, and the winds improved and allowed the fleet to sail to Troy.
Returning from the War
The Greeks, of course, ultimately prevailed over the Trojans, but it took ten years and during that time, Agamemnon's cousin returned to Mycenae to continue his family's revenge against the sons of Atreus. Aegisthus seduced Clytemnestra and the two plotted to kill Agamemnon on his return, Aegisthus wanting him dead because he was a son of Atreus, and Clytemnestra wanting him dead because he tried to sacrifice her daughter. As noted, Clytemnestra fit in well with the House of Atreus.
Agamemnon returned and, though warned by his captive Cassandra that he was in danger, ignored her warning and was subsequently murdered in the bath.
The murder of Agamemnon was ultimately avenged by his son Orestes, on orders of Apollo and with the encouragement of his daughter Electra.