The term Islamofascism strikes me as a pretty apt description of the political and religious movement of which al Qaeda, the Taliban, Hamas, and other extremist Muslim groups are members. According to the Oxford English Dictionary, "Islamofascism" is,
The advocacy or practice of a form of Islam perceived as authoritarian, intolerant, or extremist; spec. Islamic fundamentalism regarded in this way.
1990 Independent 8 Sept. 15/8 Islamic societies seem to have found it particularly hard to institutionalise divergences politically: authoritarian government, not to say ‘Islamo-fascism’, is the rule rather than the exception. 2002 National Rev. (U.S.) (Nexis) 10 Apr., You cannot deny that a brand of Islam is most certainly at war with us. You can call this brand Islamofascism, radical Islam, Wahhabism, whatever you want. 2005 N.Y. Rev. Bks. 13 Jan. 22/4 Our enemy — variously known as Islamofascism, Islamist extremism, global jihad — has no rational agenda beyond its desire to destroy the United States out of remorseless, theologically inspired hatred for its values.
The link to fascism strikes me as quite sound: It is authoritarian, in the sense of not allowing genuine democracy, suppressing speech and religious dissent, and aiming to control many aspects of people's private lives through force of law or violence (consider the Taliban regime). It is also linked to fascism's historical desire to gain political power through military conquest; not all militarism is fascist, but fascism in the 20th century has been so closely linked to militarism that fascist should probably be used in such a way that all fascism is militarist. The link to Islam is unfortunatelly also quite sound; Islamofascism is a strain of Islam, though fortunately there are many other much better strains.
The rivals strike me as suboptimal: "Islamism," which I am told is the more common academic term, is too likely to be confused with simple Islam, and seems to me to contain a more solid condemnation of Islam than the more specific term "Islamofascism" includes. "Jihadism" is a possible alternative, but raises its own problems, especially given that the term "jihad" may in some situations have nonmilitant meanings. Fortunately, "fascism" these days has a connotation that's negative beyond cavil, more so than "jihad."
And, yes, if there were Jewish or Christian movements that aimed to govern the way the Taliban did, or tried to fight the way al Qaeda does, I would of course think that Judeofascism or Christianofascism would be perfectly proper terms to label them.
UPDATE: Commenter Vovan suggests: "It is a loaded term designed specifically to include Shi'a groups that the current administration finds undesirable. A commonly accepted academic term for the developments in Sunni Islam that EV describes is Salafi, and since the groups that directly attacked United States belonged to that version of Islam, there simply isn't a need to create a new term, that not only is overly inclusive, but is intentionally misleading."
Really — no need to create a new term when the "commonly accepted academic term" Salafi is available? How many people outside a narrow sliver of the academy know what Salafi means? Plus why limit yourself to the Sunni strand, given that many critics of Islamofascism are against Shia analogs, such as the more authoritarian strands of the Iranian mullocracy? The goal is a combination of quick comprehensibility and precision, and not just precision or academic purity alone.
FURTHER UPDATE: Commenter randal writes: "What's wrong with 'militant Islam'? Oh I remember, the right thinks it's too legitimizing, believe it or not. Hence 'Islamofascism.' It's being pushed on us precisely because it comes across as sufficiently insulting to Muslims."
Actually, the commenter is mostly right, until the last word. "Militant Islam" is inadequate, I think, because it doesn't carry an important implication of "Islamo-fascism" -- that it's not only aggressive towards outsiders, but also oppressive towards its own citizens. (That's also a problem with "jihadism.")
The point of many critics of Islamo-fascism, Christopher Hitchens being just one noted example, is that Islamo-fascism isn't just a danger to the west; it's bad even for Middle Eastern women, gays, political dissenters, religious dissenters, and any other noncoformists. "Fascism" captures that; "militan[ce]" does not. So the goal is to be properly and accurately pejorative towards this strand of Islam (though not to Muslims generally).