The most vicious of the insurgent organizations the US has faced off with in Iraq is al Qaeda in Iraq, often abbreviated "AQI". Don't let the name fool you though, as they're not quite Osama bin Laden's al Qaeda. Often referred to as a "franchise" of al Qaeda, it shares some ideological connections with Osama bin Laden, the occasional communique, but two organizations do disagree on some points. In fact, AQI--the murderous group which relished in beheadings and bombed hotels in Jordan--was actually a little too violent for even al Qaeda's senior leadership. In a 2005 letter, Ayman al-Zawahiri, one of the top commanders of al Qaeda, advised Abu Musab al-Zarqawi, the head of AQI, that videos of AQI operatives beheading American contractors might be a little over the edge. (No kidding, look at bullet point #5 in that letter)
Some AQI members left to join "concerned local citizens" groups, which are local militia and police forces dedicated to fighting terrorists. Some insurgent groups actually split, with half supporting the insurgency, and half supporting the US and Iraqi government. One such group was the 1920 Revolution Brigade, which featured a spinoff group, "Hamas in Iraq" (no relation whatsoever Hamas in Gaza, though). Depending on whom you ask, either the 1920 Brigade served alongside US troops in operations against AQI in Diyala Province, or Hamas in Iraq did. I'd say most American troops really can't keep them straight. I can't imagine what the American public thinks about them.
Actually, it reminds me a little bit of...