There are three main reasons that the United States supports Israel:
1.) Regional allies are in the best interests of the U.S.
2.) The U.S. has a very influential Jewish lobby.
3.) Israel is a stable, Western style democracy that the can relate to.
To comment on some recent comments:
1.)The history of the area now called Palestine is an interesting one. Suffice it to say, for most of it's history it has been ruled by larger empires. After the Israelites, the area was ruled by the Persians, followed by the Greeks, the Romans, Arabs, Ottoman Turks, and later the British. I neither recall nor can find any evidence of a completely independent Palestine in history; the area was for much of the common era (CE, aka AD) part of a larger empire, although with varying degrees of autonomy, including between 90CE and 1099CE.
2.) Not all Arabs in Israel and the occupied territories are 'Full' Israeli citizens. Not all areas were appended completely to Israel by Israeli law. Complicated, so I'll save a more complete explanation for another day.
Oh, and blacks in America are in no way second class citizens. That may have been true 50 years ago, but not today.
3.) The Arab neighbors of Israel aren't in much of a position to help the Palestinians a great deal; they have problems of their own to deal with.
Palestinian violence only hurts their cause. At no time in history has terrorism ever been wholly successful. Take a look at Northern Ireland. The Palestinians should take a page from the book of ML King and Gandhi...passive resistance would get them so much in terms of international support, and hopefully lead to peace. Instead, as per Islamic law they claim, they choose the path of violence. Israel is no saint, and many of it's own actions should probably be condemned. But as long as we see a lot of suicide bombing, the West will have a hard time siding with them.