It does depend. In the USA, the Federal Trade Commission says that you can limit your liability for fraudulent electronic transactions that are reported within 60 days.
What if I find unauthorized transactions on my account?. - Generally, if you find unauthorized electronic check conversion on your account (or someone has fraudulently obtained your banking account information), notify your financial institution immediately. Your level of loss depends on how quickly you report the problem.
Under federal law, for unauthorized electronic check conversion, you have 60 days to report these transfers after your bank account statement containing the problem is mailed to you. If you fail to report the unauthorized transfers within this time period, you risk losing all the money in your account and the unused portion of your maximum line of credit for overdrafts. It’s also a good idea to report any other unauthorized transfers on your account or problems regarding any loss or theft of your checks immediately.
Contact your financial institution about any additional limits on liability they may offer.
Of course, they recognize that giving up your banking information to anybody is still dangerous. (Note: While your bank is investigating if the withdrawals were legal, you may not have access to your account or the money that should be in it. This can last from 45-90 days. (FDIC: laws and regulations))
Be especially cautious about sharing your bank and checking account numbers. Do not give out personal information – particularly on the telephone, by e-mail or otherwise online – unless you have initiated the contact or know who you’re dealing with. Scam artists can use your personal information to commit fraud – such as identity theft. That’s where someone uses your personal information, such as your checking account number, Social Security number, mother’s maiden name, or birth date, without your knowledge or permission, to commit fraud or theft.
These recommendations are based on the Electronic Funds Transfer act, the details of which can be found here. It might be as little as $50.