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I’d say pretty safe, especially with the advent of multi-factor authentication. Of course, nothing is completely secure. A lot of it depends on the practices of the user/customer - after all the most popular password is 12345678 (or something equally lame). The most successful attack is probably phishing, which fools victims into giving out their own information. This article should give you some more information - hope it is helpful: http://resources.infosecinstitute.com/modern-online-banking-cyber-crime/
BTW, I'm not sure how this applies to countries outside of the North America and the EU.