Rumor is the American English spelling of the noun meaning a piece of unverified information of uncertain origin. Rumour is the preferred spelling in all other major varieties of English.
Examples
For example, these American publications spell the word rumor:
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]
And these non-U.S. publications prefer rumour:
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]
First came the earthquake, then the tsunami and now there’s a storm of speculation, myth and rumour. [Sydney Morning Herald]

