vicious circle = 2,430,000 hits
vicious cycle = 2,111,000 hits
According to Garner's Modern American Usage, "Vicious circle is the phrase with the stronger precedent to support it. The OED records it from 1792 in the sense 'a situation in which an action and reaction intensify each other.' Vicious cycle isn't recorded in the OED."
Garner is more accepting than the Oxford English Dictionary. He says that both forms are okay. However, he notes, "vicious circle is about 40% more common than vicious cycle in modern print sources."
Apparently, Internet users aren't as partial toward "circle" as Garner's print sources.