I hope I might be able to help you with this question.

The close-knit Israel-US relationship that we know today arises from the Cold War and specifically the Six Day War, from which Israel emerged as a regional power. The United States saw in Israel a country that fulfilled many of the qualities they sought in an ally: it shared Western values, it was militarily powerful, and it existed in a critical region of the world.

As you may already be familiar with, the Cold War was a struggle between the US and USSR in which both sought to expand their influence in the world. The Korean and Vietnam Wars were fought to keep Soviet influence out of Asia, NATO was formed to keep the Soviets out of Europe, and the US saw Israel as the key to keep the Soviets out of the Middle East. There is a book called "The $36 Billion Bargain" that talks about the US decision making process in more details. Basically they can give (post the 1979 Camp David Accords) Israel $3 billion a year to do the same job as NATO which costs the US a lot more. Just by simple math it makes sense.

I might add that unlike other US allies in the region such as Bahrain, Turkey, and Egypt Israel doesn't need to be coaxed or cajoled into being a US ally, they have always been friendly toward the United States because of their shared values. Israel was instrumental in keeping the US ally King Abdullah of Jordan in power when Syria tried to dethrone him.

Fast forward to the modern era in which the Cold War is over but the US desire to have influence in the Middle East is more important than ever. US forces use Israel as a staging ground and port, and they share technology and intelligence.

''I could not have procured the intelligence . . . with five CIAs,'' -General George F. Keegan on Israeli assistance regarding Soviet Air capabilities.

US and Israeli armies and police train together, develop new technologies (such as the Iron Dome and the Emergency bandage) and so forth. This allows the US to operate more effectively against terrorism and project power in the Middle East.

In summary:

"Israel is the largest American aircraft carrier in the world that cannot be sunk, does not carry even one American soldier, and is located in a critical region for American national security." -Alexander M. Haig, US Secretary of State