But what are the arguments in each case? Are the risks of action outweighed by the risks of inaction? Or will inaction lead to inertia and greater dangers?
It is essential to grasp the fact that the United States was radicalised by the events of 11 September. President Bush regards those attacks a modern Pearl Harbour which requires a matching response.
Whatever other parts of the world might say - and many parts of the world are saying a lot - the Bush administration feels that it has a historic responsibility.
It does not mean that Mr Bush will go to war at every turn. It does mean that he has objectives. War might be one way of meeting them, as in Afghanistan, but there are other ways and each case will be different.
Threats are part of the strategy. Threats backed up with credible power are very effective in international diplomacy. Opponents can be frightened into behaving as you want them to.
This is, of course, unfinished business for the Bush dynasty. George senior left Saddam alone when the US army had an open road to Baghdad at the end of the Gulf War. George junior would love to finish the job.
However, he knows that the Saudis are opposed to an attack on Iraq and he cannot therefore use Saudi bases for that.
He could use aircraft carriers and long range bombers, but up until now, Bush has resisted the concept of a frontal assault and has favoured economic and diplomatic pressure.
This could even be having an effect, with Iraq now talking again about "unconditional" talks with the United Nations, possibly signalling a readiness to discuss letting weapons inspectors in again - a key American demand.
There are other pressures which can be built up too - support for Iraqi opposition groups and the Kurds in the north, for example.
The problem is that all this has been going on for years with no effect. President Bush might be tempted to go for something more dramatic, such as the bombing of Iraqi arsenals.
He might reckon that the Saudis would complain publicly but rejoice privately.
Washington is worried that Iran is developing missiles and that it is helping groups like Hezbollah and Hamas which are hostile to Israel. Both groups were mentioned in the State of the Union speech.
Mr Bush does not trust the entrenched Islamist leadership which still exercise control despite the growth of some moderate elements.
The immediate accusation has been that Tehran allowed al-Qaeda fighters to escape from neighbouring Afghanistan.
An attack on Iran is most unlikely - but expect a hard-headed view that opposing extremists is more profitable in the long run than simply encouraging the weaker moderates.
It was the approach President Reagan took with Russia and that, for Mr Bush, says a lot.
The Clinton administration tried dialogue and encouragement.
Bush has not given up entirely but is not convinced that the North Koreans have changed. Washington accuses them of exporting rocket technology regardless.
In this case, threats and deterrence are part of the mix. Direct military action would only be used as a last resort as it would precipitate a war on the Korean peninsula.
Middle East issues
There is another reason for Mr Bush to highlight the threat from all three countries - all three are active in missile development and it helps to justify his own plans for ballistic missile defence.
In all this, the Americans have also swung more clearly behind the Israelis. The naming of Hezbollah and Hamas in the speech was a sign of that.
It results from a sense of exasperation about Yasser Arafat and what the Americans feel is his inability to get a grip on his people. Until and unless he stops the bombers (even he himself has called them " terrorists"), he will be cold shouldered by the Americans.
The Palestinians say this is unproductive and so do many Europeans.
But the attitude in America these days is hard.
This is not a listening administration. It is one which is acting on a belief that problems boldly confronted can sometimes be solved more easily than problems simply discussed.
There is a risk to this - such problems can thereby be made worse. It is the eternal dilemma of world affairs.