Yesterday, I walked into a branch of Washington Mutual Inc. (WM) and I noticed fliers all over showing a screenshot of a phishing email with a recommendation underneath suggesting that account holders open up a second account just for eBay (EBAY) and Paypal. They make this recommendation so that if the account holder does become a victim, they would only lose [hopefully on a temporary basis] what is in the special second account.
This is probably a good idea as long as your accounts aren't linked for overdraft purposes. There are two types of 'linking' that banks do. One type of linking is aggregating all your accounts to see if you keep a total amount of funds with the bank above a certain limit to avoid fees and get other benefits. This linking is OK. The other linking means that if you overdraw your checking account, then any other checking or savings accounts you have with the bank that are linked to that checking account would be used to cover any overdrawn checks. I have a friend who had around $5,000 in a checking account and two $20,000 savings accounts, all linked, completely wiped out. [This was actually due to a stolen debit card, not phishing, but it's still the same concept.]
I think WaMu has a good idea. In addition, it's also a good idea to use a credit card with a low limit to use for online purchases. I have a VISA card that has a limit of only about $1,000. If someone gets a hold of that number and tries to buy a $2,000 flat panel TV, a $3,000 necklace, or a $4,000 cruise, then too bad for the bad guy.