It seems to stem from two or maybe three real phenomena. The first is the presence of sharia courts in some places in Europe. In the United Kingdom, for example, "Muslim Arbitration Tribunals" are officially mandated but set up outside the court system and can resolve civil and family issues through Islamic law; there are also reports of informal religious courts. There are similar Jewish courts in Britain, and the Muslim tribunals have received encouragement from figures including then-Archbishop of Canterbury Rowan Williams. On the other hand, there are convincing arguments that the courts can sometimes be bad for women. (There's a fascinating echo of the Ottoman empire's "millet" system, in which non-Muslims were allowed to set up their own courts to deal with matters of personal law.)
The second real phenomena is the rise of vigilante sharia squads in some places. For example, in Whitechapel, East London, CNN reported on bands of Muslim men who try to keep alcohol out of the area and harangue passers-by about morality. RedState's Erick Erickson thinks he's caught CNN red-handed: While the network criticizes Jindal for not knowing of any real no-go zones, CNN itself reported on one! But the analogy doesn't quite hold. What's happening here is disturbing, but well-short of extremist-run enclaves. These are just ad-hoc groups, and area Muslims by and large condemn it in CNN's reporting. There's no evidence that these squads are powerful or widespread.
The third factor is what are known as "Zones Urbaines Sensibles," or "sensitive urban zones," in France. These areas are defined by their socioeconomic status—they're characterized by high unemployment, high rates of public housing, and low educational attainment. As it happens, many of these areas are populated largely by poor immigrants from the Muslim world, creating a neat but misleading correlation. Some of the "no-go" coverage has suggested that police and other emergency services dare not go into these areas. The United States is sadly not immune to dangerous city areas where emergency-service providers feel unsafe, so in that way this is a universal phenomenon. But as BusinessWeek notes, it's not the case that the government has written these zones off; in fact, they've been designated for further attention and work on urban renewal.
Tracing the meme to the writings of Daniel Pipes early last decade, Graham notes that the idea has since been spreading online, through people participating in social networks ideologically predisposed to this belief.
If you dig through the fever swamps of the Internet, you can see the idea spreading since then. For example, the blog "Violence Against Whites" chronicles the SUZs and other alleged no-go zones across Western Europe. (Other material on the site includes claims that Boers were ethnically cleansed in South Africa and a section on "white martyrs.") Catholic.org reports, "These areas are Muslim-dominated neighborhoods. Non-Muslims dare not set foot into the areas."
I noted earlier that there are popular misestimates of population, based on non-random and inaccurate samplings. Graham notes, depressingly, that phenomena like these are often resistant to correction.
Erroneous beliefs such as these tend to concentrate along people's partisan or ideological axes. (The same is true of liberal media, though not in this particular case.) And once an idea has taken seed, it's extremely difficult to root out. As political scientists Brendan Nyhan and Jason Reifler have shown, corrections can actually backfire, increasing holders' faith in their incorrect beliefs.
And yet, this needs to be done.