Bear with me on this one, dear readers.
I know it looks like things in the Middle East are pretty bad. No doubt, they're certainly not rosy. 2001 was the beginning of the US-Jihadist war--at least, it was the year the US acknowledged it was fighting the war in full. Jihadists had been preparing to try to boot the US out of the Middle East and create a caliphate for a long time, and were certainly at war with us in the 1990's. Nevertheless, things seem to have gone downhill in the last decade, but I argue that, for the most part, the US is much more secure in its geopolitical aspirations in the Middle East now than it was in 2000.
In general, the United States has essentially eliminated or isolate its state-side enemies, and solidified its state-side allies. It is setting up a coalition of states to take over the "front-line" management of the Middle East, so the US can do what it does best--sit back and use military/economic spending and incentives to relatively cheaply and easily pull the right levers. Let's go bit by bit.
Enemies and Former Enemies of the United States
Iran: Once a very powerful influence in the Middle East, Iran has become largely isolated. Its influence has indeed grown in Iraq, but has greatly shrunk elsewhere. Syria, once Iran's pet ally, has asserted itself as an independent force, and is leaning Westward after a diplomatic push by Bush, Blair, and Sarkozy. Iran's hand in Hezbollah is much weaker than it used to be, as much of Hezbollah turns towards legitimate government. Its control of Hamas remains relatively strong, but Hamas appears relatively deradicalized--at least for now. There is little that Iran can do to grow its influence or break the influence of the US and Israel in the region, and this is in part why it has pushed so hard for its nuclear weapons program in a short time--if it can threaten nuclear deterrence, Iran can be more aggressive about pushing outward. Ultimately, its aggressive nuclear behavior has been used by the West to isolate it in its region. Even Russia and China, who see Iran as an opportunity to irritate the US, will stop short of allowing a nuclear weapons program to arise. Further, Iran's internal unrest is growing by the month, and the regime has, as a whole, lost a great deal of influence in its own borders. Iran will retreat into the future as it turns inward or goes progressive.
Syria: Once one of the "junior members" of the Axis of Evil, Syria was heavily courted by the West (in particular by some impressive Diplomacy by President Sarkozy). While not a doll of the West, Syria has largely ceased to be a problem. The Cedar Revolution of 2005 mostly booted Syria from its control of Lebanon, creating a state that the West is trying to turn into an ally. Syria has further divorced itself from Iran, hoping to be a part of the Western economy rather than an ideological empire run by Iran. Frankly, this was not a difficult win.
Iraq: While still riddled with problems, Iraq now stands as a relatively moderate country in the Middle East that will be able to eventually play balancing games between various Middle Eastern rivals. If the next election goes well, it will be a symbol of the effectiveness of US power and determination.
Afghanistan: While certainly much farther than Iraq, the Afghani Taliban are at least destabilized and desperate; a peace deal may yet be possible. Such a deal would make Afghanistan, if far from perfect, a much more acceptable risk.
The West Bank: While not quite its own state, the West Bank has grown much more moderate over time, despite Israeli-Gaza tensions and settlement/wall building by Israel in its territory. Such a moderate takeover is a significant gift to American foreign policymakers.
Libya: Once a major nuclear arms worry, Libya has quieted down significantly, largely in the hopes of regaining Western investment and trade, but largely in the hopes of staying off the United States' radar. For all the apparent recklessness of the war in Iraq, the invasion of Baghdad showed that the United States was (at least under Bush) willing to ignore international opinion and bring down the hammer of regime change to any state regime that seriously threatened US interests, even with shaky evidence. Qaddafi, in one of his wiser decisions as Brotherly Leader and Guide of the Revolution (yes, that is his title), decided to voluntarily give up his own WMD program and welcome polite UN weapons inspectors into his country, rather than American Marines. Once a "junior member" of the Axis of Evil, Libya is working on turning into a major Western trade partner.
Friends of the United States
Turkey, Egypt, Jordan, Kuwait, Saudi Arabia, Pakistan, Yemen: These states, while also torn internally, remain steadfastly supportive of US interests in the Middle East (though not usually out of some twisted sense of altruism). But amazingly enough, the US has managed to keep the governments of these states distinctly pro-American despite overwhelming negative attitudes among the populous towards the US. Turkey is leading negotiations with non-state actors like the Palestinians, the Taliban, and Hezbollah (and is turning into, frankly, a strange Euro-Asian state that may have influence in both areas). Egypt, additionally, is keeping a lid on Gaza while trying to help negotiate a lasting peace. Saudi Arabia has fought in Iraq and is trying to stabilize Yemen (though its pro-Sunni meddling in Iraq was quite detrimental). Pakistan is (half-heartedly, at least) fighting the more dangerous Taliban on its side of the AfPak border, eliminating key support for the Afghan insurgency. These states will continue to contribute to a regional order that will allow the United States to move further and further back from the Middle East over time.
The UAE and Qatar: Worth special mention due to their (somewhat) successful adaptations of Western-style market economies. If Dubai can pull itself out of debt, these states are likely to be shining examples of how liberalism and Islam can live side-by-side (and they are unlikely to harbor anti-US terrorists, to boot).
There are certainly states of worry for the US in the Middle East. Afghanistan, Lebanon, Palestine, Yemen, Somalia, Sudan, Iran, and Turkmenistan all have major internal issues that could lead to long-term negative consequences for the US, and they are worth keeping one's eyes on.
All in all, the United States' geopolitical position in the Middle East is far from the sour position most Americans think it is in, even if it is indeed in a rather poor public image position. But such if how these things work. The US has managed to lever government loyalty with the right incentives, even if not public opinion with the right rhetoric and sympathy.