Take this Warlords of Draenor phishing scam reported by Malwarebytes as an example. It starts off with an email that's formatted like a message from Blizzard saying you've won a free copy of Warlords -- which is really where you should get suspicious. Once you click on the link in the email, you're sent to a perfect copy of the Battle.net login screen where you're asked to enter your login information as well as your secret question and answer before you can redeem your free copy... but of course the scammers just run off with your info without giving you a thing.
To avoid being had, always check the header to see where an email has come from -- Blizzard emails will only come from an @blizzard.com address -- and if an offer sounds too good to be true, contact Blizzard directly to ask about it. For more tips on avoiding phishing, check out the support page on phishing scams.