My entire day is spent thinking about your money and how to steal it...
I am not Danny Ocean (I was once mistaken for George Clooney). I work as an information security consultant for a major international bank. They pay me a decent chunk of money to think like a bad guy for over 2000 hours a year so I figure out how to steal your money before they do and make sure they don't. Of the hundreds of security incidents that my department has investigated where customers lost money from their account via online methods, one was not (entirely) the fault of the account holder. So I have to tell you from direct experience our bank is secure. You, however, could use some help in securing your end.
In the physical world, after you take cash out of the bank do you shout "I JUST TOOK OUT 300$! My PIN number is 4567!!!" and leave the money on your car seat? No, of course not. You take basic precautions when you use an ATM because you do not want to become an ATM for a mugger.
Common sense and your mother always told you that before you use the ATM you look around to make sure no one is hiding in the bushes. While using the ATM you cover the keypad so only you see your PIN. Afterward you put your money in your wallet or sock and quickly go to your car. Online precautions are similar and just as easy.
Hackers go after the weak link. Since the bank is a formidable opponent (remember I work there) they prefer to go after a softer target. You and your computer fit the bill nicely. Many users have a tendency to click on links without considering where it is sending them. Combine that with web page addresses that can be disguised or take you to an unexpected site. New security vulnerabilities in computer systems and software packages often result in exponential increases in the number of attempted attacks.
Tip #1 Do not be the soft target.
Do not click on links to get to your bank site. Always use your bookmarked site. Attackers will buy websites that are close misspellings of actual sites.
Tip #2 Do not be afraid of making changes to your computer.
Many users are unwilling to enable or disable functionality as required to secure their web browser. That is OK because I will show you how to configure a separate browser just for onlne banking.
Tip #3 Never send your bank information via email or in any kind of online form.
The bank already has this information and they do not need it again. If in doubt pick up the phone and call the customer service number on the back of your ATM card.
Tip #4 Ask your bank for help.
Some banks will give you software to help secure your PC and even help you configure it. Also they can send you alerts if a large transaction is done on your credit card or checking account.