Our enemy is certainly not Islam as a whole. Yet neither is is it the radical Islam that most our enemies espouse. Were it, it would be invincible. There is no way you can defeat a person a people imbued with radical Islam. As Kevino said, no conventional police force may defend against the suicidal.
Then it is fortunate radical Islam is not the enemy. Nay, rather it is those factors that bring about the circumstances under which radical Islam thrives. Namely, the desperate conditions enjoyed by most in the Middle East: their economies are going nowhere, almost all the power, political and financial, is held by an elite few, and the populace, the majority of which are youth under 25 years of age, are going crazy at their inability to improve their lives and take control of their future. Normally, when a large segment of society loses faith in its institutions' abilities to accomadate them, they lash out at those in charge of the institutions, attempting, in an often violent and disorganized manner, to fix the system by transforming it: they revolt.
The elites in the Middle East are atleast partially if not fully aware of the situation, but they have devised a devious system of avoiding said disorder (and the fate it would bring them): they've passed the buck. Through direct support of Islam and indirect support of radical Islam, they have successfully redefined the situation in the eyes of their desperate society.
The people in charge are no longer the elites who are hogging the oil while repressing reform and political dissent. Nay, it is the United States. The case that we are in charge is understandably easy to make. In many ways we are. We intervene continuously militarily, support Israel, and are always telling them what to do. The case that we are thus responsible for the woes of their society is made easy once religion is mixed in: our culture is "wrong" and thus by merely having power over them taint their society, causing social problems, which in turn is why you, Joe Muslim, are dirt poor, don't have a future, and feel hopeless & desperate. In such a way the oil elites of the Middle East have successfully deflected that malcontent that has in the past been at the root of revolts from France to Russia to Iran. Most Joe Muslims subsequently fume at the United States and cheer when the footage of Hezbollah comes up. A crazy few find the resources or provide the resources to "revolt" against the United States through acts of terror and many many delusional diatribes about how Islam will rule us all.
Thus the enemy is not radical Islam. No, that is just a weapon, a particularly dangerous idea that has been manipulated as deftly as we may manipulate planes and armor in our wars. The enemy is those that have decided the satisfaction of their greed is more important than the welfare of the societies they control. An example: Those Iranian Mullahs who fund Hezbollah, rail against the United States, and advocate their nuclear program are also some of the biggest Iranian propertyholders.
Thus now that we understand the root of radical Islam and the terrorism, anti-Americanism, and, occasionally, sharia it in turn spawns, we understand also the extent and capabilities of the threat.
First, in most open societies, radical Islam cannot endure. If a populace is to support it, they must not have an economic or political stake in society (thus be poor & without a vote) and be surrounded by an institutional & media presence that supports radical Islam. Impressively, through their negligence and the hard work of Iran, such a state has nearly been achieved in many European countries, yet were they to organize politically (begin voting) they would then have a stake (but take note: not control) in society and thus no longer interested in its destruction.
Second, the elites whose greed gives radical Islam its power, being motivated by greed, are also limited by it. Thus we can be assured that Iran, upon nuclear acquisition, will not use the nukes against us, as outlined by JEM. They know that were they to do such a thing, they would lose all power at the hands of an enraged America. Indeed (granted we would never want such a thing to happen for our love of life) the use of a nuke would ultimately be the most positive possible development for the US. We would instantly gain full unwavering support from all other Western nations and would use our military capabilities in such a callous fashion that we would soon effectively rule the Middle East. That is not what the elites want. Like smart drug-dealers, they never buy their own product. They are not suicidal. No, the Iranian elites (they are the best example) use radical Islam and war-mongering only as a tool to control their populace (and use it effectively, as noted by Kevino, Iranian malcontent with the government has dropped dramatically since 2003, the same year they announced the nuclear program), not to actually fight the United States. They will only push it as far as they think it safe and no further. Of course, should they gain the bomb, that "safe" limit may be extended enormously, which is why we need to work against such a thing happening.
Obviously we will continue to fight terror and call radical Islam wrong wherever it crops up. But that's just playing defense. To solve the problem we need to attack the root.
So how do we fight those elites that are spawning terror & anti-Americanism so that they might safeguard their own greed?
The most obvious method is to kill off the elites and institute a free society. We're trying that in Iraq. Unfortunately, that requires enormous resources and, if improperly executed (as has happened in Iraq) might have more negative than positive consequences, atleast in the short term (I still hope for success).
A more practical approach would be to use economic & limited military pressure to force the elites to reform their society so as to redress the desperation of their citizens. In this endeavor we are limited by our dependence on oil, which makes us more dependent on them than they are on us (and prevents us from, for instance, air-striking Saudi Arabia to make a point), and that economic sanctions can be ineffective if unilateral (the case with Iran).
We can also wage a propaganda war. Again, though, we are severely limited as their elites control all mainstream means of propaganda, and they have more experience. Iraq could become a platform for a much more effective propaganda campaign, but again, that hinges on establishing a stable free society there, by no means a certainty.
Finally, we can give them the hug of death. Were we to broker a permanent peace in Israel and affected areas and tone down all other policies that may be twisted to justify radical Islam while stepping up aid programs, encouraging trade (like we have with China), condemning all Islamic rulers that do wrong, and taking advantage of opportune moments to prove our goodness (the tsunami aid is an excellent example), then we might make it impossible for them to denounce us as evil (for we do nothing but good, bring nothing but prosperity) and free the Muslim societies against their rulers will (as is happening in China).
Certainly there is no straight arrow solution, but the fourth mixed in with the other three according to the situation will probably get the trick done. To summate: radical Islam is not the enemy, rather is only the shield of greed. The elites (the rulers, politicians, bureaucrats, clerics, royal families) of the Middle East are the true enemy, for their placement of their own welfare before their societies' is what has created such perfect breeding grounds for radical Islam. As such we need not fear a global war but the anti-Americanism, terrorism, and threat to our oil supplies radical Islam produces merits our effort towards a solution. Any such solution must concentrate on the elites and reforming their societies, and although I'll hear suggestions, it promises to be complicated.If anyone has made the journey, yes, this is the same as a comment I left on vodkapundit.