What relationships do the US and Israel have in common?

The official term for the relationship between the United States and Israel is a "Special Relationship".
This relationship arises from a variety of sources. Israel has cooperated with the United States on diplomatic issues, military and intelligence exchanges, large amounts of trade, and significant technological investment. In addition there a numerous Americans who support the State of Israel because of religious convictions on top of the already-listed reasons. The United States government, therefore takes a pro-Israel stance in international politics and is often seen as Israel's backer.

Israel and the United States started on friendly terms with the United States approving the 1947 Partition Plan. However, until the Six-Day War of 1967, the United States did not see Israel as a country that would exist in the long-term because of Arab belligerence against the State. After Israel's stunning victory in that war, the United States became Israel's primary Western Ally and began to trade technologies, both civilian and military, with Israel.