(Captain's log): If indeed Arafat dies, and if indeed this finally polarizes the nations and forces them to show their true colors, then this is my best guess as to how the various nations will end up in the struggle. I categorize them into eight groups.
Level 3 friends: These are nations which will fight beside us (the United States), who will commit fully to the war, and whose help we will be grateful to have. There will be no doubts about their friendship once this is over. Canada, Australia, the UK
Level 2 friends: These nations will make a substantial commitment and will definitely align with us, but will mostly make a passive contribution e.g. basing privileges, intelligence, diplomatic support. If parts of the war are fought in their territory, they will be involved: Israel, Qatar, Oman, Pakistan, India, Japan, Kuwait?, Turkey, some of the 'stans, Georgia, Poland, The Czech Republic, New Zealand
Level 1 friends: Basically friendly bystanders, they won't do anything to impede us but also won't contribute a great deal to the struggle; some intelligence, perhaps; cooperation in hunting down spies and terrorists, maybe a handful of non-combat troops, but not really a great deal that matters: The Netherlands, Germany, the Scandinavian nations, Spain, Italy, Portugal, Russia?, The Philippines?, Indonesia?, Latin America (except Cuba), South Korea, Taiwan, Jordan?, the rest of the 'stans, the Baltic republics, Ireland, Switzerland
Neutrals: Occasionally impeding us, occasionally helping us, but never really making much difference either way, these nations won't matter: France?, China?, UAE, SE Asia (i.e. Thailand, Viet Nam et al), Greece, Belgium, Balkan nations (i.e. Romania, Slovenia et al), Ukraine, Belarus, Mongolia, Bangladesh, Hungary, Slovakia, Austria
Level 1 enemies: Nasty looks in our direction and doing their best to put sand into the diplomatic gears but in practice making little difference: Cuba, African Muslim nations (except Libya) including Egypt?, sub-Saharan Africa, North Korea
Level 2 enemies: Actively working against us but not directly involved in the combat: Lebanon, Libya?, Yemen
Level 3 enemies: Before we're through, all the governments of these nations will have to be replaced one way or another, and they'll probably have to be occupied. Saudi Arabia, Syria, Iraq, Iran, the Palestinians?, (the Taliban)
Anarchies: These are places without governments. They may end up being battlefields. Afghanistan, Somalia
The nations with question marks are difficult to judge. I've placed them where I expect to find them. Kuwait may drop to a level 1 friend. Jordan might become a level 1 enemy. The Philippines and Indonesia could drop to neutral. France could be anywhere between a level 1 friend and a level 1 enemy. China might drop to a level 1 enemy. Russia might rise to become a level 2 friend. Libya may turn out to be a level 3 enemy. The Palestinians may end up being level 2 enemies, as could Egypt.
Localized conflict will take place between Israel and the Palestinians for the duration of the war until outsiders become directly involved and impose a peace. They will, for the most part, nullify each other.
This is, of course, highly speculative and subject to change as events unfold. For example, a major terrorist attack (WTC-scale) in a G7 European nation would probably make it a level 3 friend and probably would cause most of the other western European nations to move up one notch. If Israel ends up using a nuke, most of the Arab nations drop at least one notch and most of the L1 Europeans will drop to neutral. If Iraq uses WMDs, a lot of nations rise one step.
A real shooting war between Pakistan and India turns both into neutrals or L1 enemies.
The governments of some nations are shaky and if they change peacefully or via revolt then it's difficult to say where they would land afterwards. The one I'm least confident in is Pakistan, which could lapse into civil war at any time. The fate of its nukes becomes a serious concern, and in case the Musharraf government becomes seriously threatened, it would probably be necessary to commit troops to stabilize it, or to capture its nuclear arsenal.
Update: Oh, by the way; I don't think that the EU or NATO as such (as opposed to their member nations) will make any difference one way or the other. NATO would rank as a level 1 friend; the EU as the same level as France ends up being. By the same token, the UN effectively becomes a level 1 enemy.