Even if it isn't the most important theme in Agamemnon, "Family" is definitely up there because it provides the context for everything else. Let's not forget that everything in Agamemnon goes back to the generation before the main action takes place, when Thyestes had an affair with Atreus's wife; in revenge, Atreus killed Thyestes's children, butchered them, and served them to him for dinner. Atreus, of course, was Agamemnon's father; at the end of the play, when Aegisthus, one of Thyestes's remaining children, shows up on stage, he remarks how the murder of Agamemnon convinces him that the gods are just.
But Aegisthus didn't kill Agamemnon himself, right? (We don't know for sure, but it doesn't seem like he had a hand in it.) The actual murder was committed by Clytemnestra, who was angry because Agamemnon sacrificed their daughter, Iphigenia; thus, you could say that Clytemnestra killed Agamemnon to defend her family. At the same time, various theories get put forward by different characters (especially the Chorus) about how a curse on Agamemnon's family was responsible for making him sacrifice his daughter, or even that his father's bad behavior set a bad example for his son, and his homicidal tendencies got passed on that way. Thus, Aeschylus's play also gets into some very modern issues about how human characteristics get passed on from generation to generation.
The fact that Menelaus gets off scot free shows that, when the Chorus talks about a supernatural spirit of vengeance inhabiting the house, that is really just a metaphor for the anger felt by Clytemnestra and Aegisthus.
Clytemnestra's inconsistent behavior towards her children (mourning Iphigenia, banishing Orestes) suggests that anger over her slain daughter isn't her real motivation for killing Agamemnon.