Some excellent advice is given in this article from PC Pro magazine:

Beat the scammers

Most scams, however, can still be foiled by asking yourself a few questions. Would you give your bank account details to a stranger over the telephone? Does Visa need reminding of your credit card details? How many high-ranking Nigerian government officials would trust their millions with you? How much cash have you put into improbable schemes that promise to double your money in six months?

You're probably thinking that the answers to these are no-brainers, and you'd be right in the physical world. Unfortunately, when you move the same ridiculous scenarios into the online world, common sense often seems to fly out of the window. Otherwise streetwise and sensible people become naive, gullible and prey to one of the biggest curses of the Internet age: the Dot Con.