Nobody can access your account because they have your checking account number. If that were true, you could never write a check for anything. Everyone you have ever paid by check could have your account number and the bank routing information.
The biggest risk you have is debit cards. Because if someone scams your number and pin they can clean you out. Every thing else requires a signature. One other precaution you can take is to remove the 3 digit code on the back of your credit cards. They can be scrapped off with a knife. Then no one can use it for internet purchases. Record them in a safe place prior to removing, just in case you want to use it for an internet purchase.
When using a debit card in any machine, store check out, ATM, any place you swipe the card, make sure there is nothing strange about the machine. Most common way to steal your information is a reader mounted on the ATM where you slide your card in. Many ATM's now have a green led light ring around that slot so if it is cover over by an external reader it is obvious. But thieves can install a thin reader over the slot and you really can't tell with out looking closely.
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Life is to short to drink cheap wine.
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