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From here: http://www.snopes.com/fraud/phishing/hotel.asp

Origins: This helpful heads up has been circulating on the Internet since January 2008.

The switchboards of most reputable hotels follow a policy of not connecting incoming calls to guests' rooms unless callers can supply the guests' name. (Some hotels take that policy
an extra step by requiring both guests' names and room numbers before putting through outside calls.) Therefore, while the advice about not giving out one's credit card information to anyone who telephones to ask for it is always worth heeding, in this particular instance, the warning that encompasses it is a bit overblown. Those looking to "phish" your credit card number and the 3-digit security code carried on its back by pretending to be working at the front desk aren't going to be able to smoothly run this con at hotel after hotel, because most places they telephone will refuse to put their calls through — their demands to be connected to "Room 620" will be stonewalled by those managing the property's switchboard unless and until they can also pony up the right name that matches with the hotel's records of who is staying in that room.

However, that this policy is widespread doesn't mean every hotel in existence observes it or that a particularly charming scam artist couldn't occasionally succeed in wheedling a gullible hotel switchboard operator into putting through a call on the basis of a bare room number and nothing else. Also, some hotels allow guests to direct dial to other rooms, which means a con artist who took up residence in such an establishment could potentially run this fraud on others staying there. It is therefore a good idea to always be mindful of the potential for fraud and to make it your own personal policy to never give out credit card information to anyone who calls asking for it, no matter who that person claims to be. In the case of hotel stays, that means not providing such information to the caller, but rather making a trip down to the front desk, or at the very least placing your own call to that facility to ask if there's a problem with your card.