Favor and favour are different spellings of the same word. Favor is the preferred spelling in American English. Favour is preferred in all other varieties of English.
Examples
For example, these non-U.S. publications favor favour:
Punters have written off Julia Gillard in favour of former union boss Bill Shorten and backed the coalition to win the next federal election. [The Age]
And that means Ferguson will urge Birmingham City to do him a favour against Arsenal. [Guardian]
The Supreme Court evidently favours a co-operative approach. [Globe and Mail]
The opposition Congress twice staged a walkout from the Chhattisgarh Assembly today over the alleged favour shown by the state government … [MSN India]
And these American news outlets use favor:
The intent of a system that favors the youngest and the healthiest is to ensure the best and longest use of donated kidneys. [New York Times]
71% oppose increasing sales, income or other taxes while 27% are in favor that approach. [USA Today]
Torres knew Chang was associated with the Giants but did not know he was an owner and asked for a favor. [San Francisco Chronicle]
