There is really only one major reason for the United States to have much of an interest in the Persian Gulf and that is the fact that the area around the Persian Gulf has much of the world's deposits of petroleum.
Petroleum, of course, is the raw material that gets made into diesel, gasoline, jet fuel, plastic, many fertilizers, and a whole host of other things that are absolutely necessary for life in today's world.
Because petroleum is vital to the US economy, it is in the interests of the US to try to maintain stability in the area and good relations with countries such as Saudi Arabia.
The previous posts are right. While I wish the answer could be more patriotic, more flowery, and even more poetic, the answer is the very name of the Upton Sinclair work: Oil. The presence of petroleum in the region has continued and will continue to keep the United States' presence a dominant one in the region. In the past decade, there has been justification made on the grounds of terrorism and fighting it as the primary reason why the United States has interest in Saudi Arabia, in particular. Proponents of this logic point to the fact that an overwhelming number of the hijackers on September 11 were of Saudi descent, and that there are a number of terrorist organizations in the region. However, this does not remove the underscoring rationale of the protection of oil and interests of the United States in the region. The policy of the United States towards Saudi Arabia and this region has been driven by economic interests for quite some time, and recent claims of fighting terrorism do little to remove this guiding interest.
Oil most certainly, since Saudi Arabia, Iraq and Kuwait combined hold almost 40% of the world's known oil reserves. In addition, we have a major interest in Saudi Arabia in that, as their best customer, we have a stable, mutually beneficial relationship. They act as one of our only Arab allies in the region, have allowed us to use the Kingdom for a military base at times, and have, at least in some ways, given us aid in the war on terror.
Remember that Osama bin Laden is Saudi Arabian, and al-Qaeda was born in that country. So the government of that nation have just as much interest in seeing him captured and his terror network dismantled as the US does.
One of the two major reasons is the Middle East has the largest petroleum reserves in the world. The US receives much of its oil from Middle Eastern countries and hence requires a major interest. The other is security instability between Israel and its neighbors. The US considers Israel its chief ally in the region and relies on its intelligence services for information concerning world security matters.