For a more systematic look at the common intellectual roots of European fascism and radical islamism, discussed in David Bernstein's recent post, check out Ian Buruma and Avishai Margalit's book Occidentalism: The West through the Eyes of its Enemies. As the authors point out, both fascism and radical Islamism were heavily influenced by the nineteenth century European romantic nationalist reaction against liberalism and free markets. The romantic nationalists claimed that liberal society was overly materialistic, neglected important group ties, and lacked spiritual values. Obviously, the fascists were direct intellectual descendants of the romantic nationalists, whose ideology they took to new extremes. In the Arab Middle East, the intellectual connection emerged as a result of the penetration of European nationalist ideas beginning with the early twentieth century.
In the 1930s, as historian Bernard Lewis explains here, Nazi Germany made a "concerted effort" to export its ideology to the Arab world directly; they were in large part successful. Many of the Nazi ideas were taken up by the early radical Islamists at that time, as German scholar Matthias Kuntzel discusses here.
I would add that the modern radical Islamist version of anti-Semitism also has its roots in European nationalist and fascist thought. This is most clear in its embrace of the Protocols of the Elders of Zion, a forgery created by czarist Russian secret police and first popularized by right-wing Russian nationalists. As the NY Times puts it, the Protocols have become a "canonical text" for radical Islamists. More generally, the entire idea that the Jews are a powerful, insidious cabal dominating capitalist economic system is rooted in European nationalist and fascist ideology and is very different from traditional pre-20th century Muslim anti-Semitism (which viewed Jews more as objects of contempt than fear). There are some important differences between fascist and radical Islamist ideology. Perhaps the most important is that the latter is an internationalist ideology that cuts across different racial and ethnic groups, while the former tries to exalt a particular nation-state. But they also have numerous commonalities, including strikingly similar reasons for their hatred of liberalism, democracy, the free market, and Jews.
UPDATE: To avoid confusion, I should emphasize that this post is not a defense of the term "Islamofascist." It's a post on the intellectual roots of radical Islamism, many of which are fascist in origin. For what it's worth, I think the term is on balance counterproductive. It tends to alienate liberal Muslims (a key constituency the US must appeal to), while largely failing in the original objective of rallying Western left-wing support for the War on Terror, as David noted in his post. At the same time, the term is descriptively accurate as a characterization of the ideology of Al Qaeda and other similar groups. That ideology does indeed combine a reactionary strain of Islam with major elements of European fascism. Sometimes, the use of a word is both accurate and tactically unwise.