Rumor is the U.S. spelling of the noun meaning a piece of unverified information of uncertain origin. Rumour is the preferred spelling in all other main varieties of English.
The government then launched a massive crackdown on hoarding, price-gouging and rumor-mongering. [Los Angeles Times]
The freshest iPhone 5 rumor has nothing to do with a larger screen. [Fortune]
Outside the U.S.
It’s the rumour that simply will not die. [This is London]
Widespread rumours suggested the Internet retailer also might launch a branded smartphone in 2012. [Montreal Gazette (article now offline)]
First came the earthquake, then the tsunami and now there’s a storm of speculation, myth and rumour. [Sydney Morning Herald]