For the verb meaning to work or act together, American writers use the unhyphenated cooperate. Outside the U.S. co-operate, with a hyphen, is preferred. Neither spelling is better than the other. There is good justification for the hyphen (it prevents pronunciation confusion), but fluent English speakers have no trouble understanding what is meant by the unhyphenated form. The American spelling would cause trouble if there were a word in English pronounced KOO-perate, but there isn’t one.
The spelling preference extends to all derivatives of cooperate/co-operate, including cooperation/co-operation and cooperating/co-operating.
American publications prefer cooperate:
The foreign ministers of Iran and Turkey pledged Friday to cooperate against ethnic Kurdish rebels. [Los Angeles Times]
Cooperation, that fine art of working together toward a common goal, is more appealing to children than to chimpanzees. [New York Times]
Mr. Kumar pleaded guilty to securities fraud and conspiracy, cooperated, and is awaiting sentencing. [Wall Street Journal]
And though cooperate is fairly common outside the U.S., co-operate is preferred:
In a strategic pact signed on Tuesday, the two countries pledged to co-operate on trade and counter-terrorism. [Guardian]
In a deal that may signal future co-operation between enemies, Israel and the militant Palestinian movement Hamas have agreed to an exchange of prisoners. [Globe and Mail]
Mobile-phone retailers haven’t co-operated in the past, Gartenberg said. [New Zealand Herald]