As some others here, I have a checking account with a debit card that I use for all day-to-day purchases. I keep a relatively small amount of money in it, re-stocking as needed from my principle account. The primary account, which receives all my direct deposits and received checks, has no card or PIN associated with it - the only access is through the bank's website, with a secure password. So anyone stealing my shopping card info is picking a very shallow pocket. It's not a solution but a reasonable safeguard.
As far as credit card frauds, I've only had one. They notified me of a questionable purchase and had me fill out a form denying the claim. The charge was erased and nothing further was said. I don't know if they ever found the offender - I hope they did.
For online purchases, I use a generated virtual card number. It's a slightly irritating second step, but does make me feel better.