Genesis 12:3 and 18:18 say that the nations will be blessed through Abraham, and 28:14 says that all the families of the earth will be blessed through Jacob's seed. Genesis 22:18 says that all the nations shall bless themselves through Abraham's seed, and 26:4 says the same about Isaac's seed.
Paul in Galatians 3:8 applies Genesis 12:3 to Jesus Christ, the seed of Abraham, though whom the Gentiles would be blessed. When I was first exposed to the method of reading the writings of the Hebrew Bible in light of their contexts, not later Christian interpretations, I wondered how I should interpret Genesis 12:3. How would Abraham bless the nations? Some translations took the niphal in Genesis 12:3, nivrechu, as "bless themselves." In that case, how would the nations bless themselves?
At Harvard Divinity School, Gary Anderson presented the interpretation that "bless themselves" in Genesis 22:18 (I think that was the reference he cited, but it could have been Genesis 12:3) means that the nations would see how blessed Abraham is and wish the same sort of blessings upon themselves: May we be as blessed as Abraham's seed.
In Judaism, I've encountered Jews who view Genesis 12:3 as a sort of mission statement for them to do good to others and to demonstrate the character of God. I think of Jewish musician Debbie Friedman's song, "Lech Lecha," which includes the line, "and you shall be a blessing, and you shall be a blessing, and you shall be a blessing, lech lecha."
When I first attempted to read Genesis 12:3 from a contextual standpoint---reading Genesis in light of Genesis, rather than Christian interpretations---I thought that maybe the passage was saying that the Gentiles would be drawn to God when they saw Abraham's character, or God's blessing upon Abraham and his seed. But I had a couple of problems with this view. First of all, it wasn't explicitly stated in Genesis. And, second, I wondered if the Hebrew Bible contained the message that Israel existed primarily to bring the Gentiles to God. Granted, there are plenty of passages about Gentiles acknowledging the greatness of God---and I guess that Second Isaiah leans in that direction. But I just wondered if Judaism had the same missionary impulse that evangelical Christians possess.
My colleague at Hebrew Union College, Ben Noonan, has an article in Hebrew Studies 51 (2010), entitled "Abraham, Blessing, and the Nations." Ben knocks down plenty of sacred cows. He disputes the notion that nivrechu in Genesis 12:3 means "bless themselves," by looking at the use of the niphal in the Hebrew Bible. He also disagrees with the view that the hitpael in Genesis 22:18 and 26:4 has to mean that the nations will pronounce a blessing on themselves when they see the prosperity of Abraham's seed---wishing to be as prosperous as the Israelites. He takes a look at the other places in the Hebrew Bible that use the hitpael of b-r-k (Deuteronomy 29:19; Psalm 72:17; Isaiah 65:16; Jeremiah 4:2), and he concludes that, in Genesis 22:18 and 26:4, the message is that the nations will bring divine blessings upon themselves by doing good to Abraham's seed. They won't just pronounce divine blessings upon themselves by wishing to have the same prosperity as Abraham's seed, but they will actually contribute to their own blessing by doing good to God's people. After all, God promises in Genesis 12:3 to bless those who bless Abram, and to curse those who curse him.
And, throughout Genesis, God blesses nations through Abraham's seed, as Ben documents. Abraham delivers nations from oppressive kings (Genesis 14). Laban is blessed by God on account of Jacob (Genesis 30:27-30). Joseph saves Egypt and the world from death due to famine. (Ben uses some of these examples, but not others; he also refers to other examples.) Perhaps the whole idea of the nations being blessed and blessing themselves in Genesis was to highlight the importance of Abraham and his seed: they would have such an influence on the world, that nations would be blessed or cursed through them. How God treats the nations would be based on how the nations treated Israel.