Much nonsense has been written in recent years about the prospects of American decline and the inevitable rise of China. But it was not a declining power that I saw in recent weeks as I jetted from the Middle East to the Far East through two of America’s pivotal geographic commands — Central Command and Pacific Command.

The very fact that the entire world is divided up into American military commands is significant. There is no French, Indian or Brazilian equivalent — not yet even a Chinese counterpart. It is simply assumed without much comment that American soldiers will be central players in the affairs of the entire world. It is also taken for granted that a vast network of American bases will stretch from Germany to Japan — more than 700 in all, depending on how you count. They constitute a virtual American empire of Wal-Mart-style PXs, fast-food restaurants, golf courses and gyms.

There is an especially large American presence in the Middle East, one of the world’s most crisis-prone regions. For all the anti-Americanism in the Arab world, almost all the states bordering what they call the Arabian Gulf support substantial American bases. These governments are worried about the looming Iranian threat and know that only the United States can offer them protection. They are happy to deal with China, but it would never occur to a single sultan or sheik that the People’s Liberation Army will protect them from Iranian intimidation.

In the Far East, a similar dynamic prevails. All of China’s neighbors happily trade with it, but all are wary of the Middle Kingdom’s pretensions to regional hegemony. Even Vietnam, a country that handed America its worst military defeat ever, is eager to establish close ties with Washington as a counter to Beijing.

What of America’s two most important allies in Northeast Asia — South Korea and Japan? Not long ago, relations with Seoul were frosty because it was pursuing a “sunshine policy” of outreach to North Korea that the George W. Bush administration (rightly) viewed as one of the world’s most dangerous rogue states. More recently, relations with Japan became strained after the election of the Liberal Democratic Party in 2009 on a platform of cozying up to China, rethinking the 50-year-old alliance between the U.S. and Japan, and moving U.S. bases out of Okinawa. Now Prime Minister Yukio Hatoyama has had to undertake an embarrassing U-turn by agreeing to an earlier plan that would move a U.S. Marine Corps air base from one part of Okinawa to another but keep it on the island.

In justifying his reversal, Hatoyama said that “we cannot afford to reduce the U.S. military deterrence” because of “political uncertainties remaining in East Asia.” There is no shortage of such uncertainties with the Chinese navy becoming increasingly assertive in moving into Japanese waters and with North Korea, which has missiles that can easily hit Japan, sinking a South Korean naval ship with the loss of 46 sailors.

The latter incident naturally has focused attention in Seoul and served to accelerate the reaffirmation of close American-Korean ties that had already begun with the election of the more conservative President Lee Myung-bak in 2008. The anti-Americanism that had been prevalent in South Korea only a few years ago has all but disappeared, and it is not only (or even mainly) because of President Obama’s vaunted charm. It is largely because South Korea has tried detente and found that it did nothing to moderate the aggressive behavior of the North Korean regime.

China is South Korea’s largest trade partner by far, but Beijing shows scant interest in reining in Kim Jong Il. The greatest fear of Chinese leaders is that North Korea will collapse, leading to a horde of refugees moving north and, eventually, the creation an American-allied regime on the Yalu River. Rather than risk this strategic calamity, China continues to prop up the crazy North Korean communists — to the growing consternation of South Koreans, who can never forget that Seoul, a city of 15 million people, is within range of what the top U.S. commander in South Korea describes as the world’s largest concentration of artillery.

South Korea knows that only the U.S. offers the deterrence needed to keep a nuclear-armed North Korea in check. That is why the South Koreans, who have one of the world’s largest militaries (655,000 activity-duty personnel), are eager to host 28,000 American troops in perpetuity and even to hand over their military forces in wartime to the command of an American four-star general. Under an agreement negotiated during the Bush administration, operational control is due to revert to the South Koreans in 2012, but senior members of the government and military told us they want to push that date back by a number of years.

South Korea’s eagerness to continue subordinating its armed forces to American control is the ultimate vote of confidence in American leadership. What other country would the South Koreans possibly entrust with the very core of their national existence? Not China, that’s for sure.

And yet South Korea is not so unusual in this regard. The Persian Gulf emirates also entrust their continued existence to America’s benign power. The Kurds, whom we visited in Irbil, are eager to host an American base, because they know that all of the gains they have made since 1991 have been made possible by American protection. Even Arab Iraqi politicians, who traffic in nationalist slogans while running for office, are quietly talking about renegotiating the accord that would bring the U.S. troop presence in Iraq down to zero by the end of 2011. They know what Kosovars, Kuwaitis and countless others have learned over many decades: American power is the world’s best guarantor of freedom and prosperity.

This isn’t to deny the prevalence of anti-Americanism even in the Age of Obama. Nor is it to wish away the real threats to American power — from external challenges ( Iran, China, Islamist terrorists) to, more worrying, internal weaknesses (rising debt levels, decreasing military spending as a percentage of the federal budget, a shrinking Navy). But if my cross-global jaunt taught me anything, it is that those countries that dismiss the prospects for continuing American leadership do so at their peril. The U.S. still possesses unprecedented power projection capabilities, and, just as important, it is armed with the goodwill of countless countries that know the U.S. offers protection from local bullies. They may resent us, but they fear their neighbors, and that’s the ultimate buttress of our status as the world’s sole superpower.

Max Boot is the Jeane J. Kirkpatrick senior fellow for national security studies at the Council on Foreign Relations and a contributing editor to Opinion.