I woudn't be so convinced that the non-randomized nature of online polls only introduces moderate bias -- little enough that lopsided results accurately refelect the general opinions you'd see from a representative survey.

Ballot stuffing is a huge part of online polls now. I look at a variety of political blogs, and calls to "Freep" this or that poll are now quite standard (called "Freeping" because it was FreeRepublic that first turned it into a science, but you see calls all the time at dKos, etc too).

In one of most egregious cases, Time Magazine did online polls for "Man of the Century" and other subcategories in 1999. Due to a very organized campaign in Turkey, Kemal Attaturk was the runaway leading candidate for Man of the Century, as well as Scientist of the Century, Poet of the Century, Rock Star of the Century, Woman of the Century, etc.

Or ask the Literary Digest, the magazine that was famous for doing a write-in reader poll to predict presidential elections. After receiving 2.3 million responses, they reported that FDR was headed to a humiliating defeat in 1936. George Gallup, with a thousand or so people in scientifically conducted randomized polling, correctly saw FDR's upcoming landlside reelection.