DON'T CANCEL ALL YOUR CARDS!!!!
At least not at all lightly.
Dave Ramsey forgive me.
Your credit score can nuked if you do that.
Once you have an account with anyone it's better not to cancel it unless you have to, you can monitor these things relatively well and also most cards have features that will email alert you to any charges over x.
If you have a complete breach of your information then someone could start opening accounts in your name which is what the monitoring will alert you to, any new inquiries and any new accounts will show up quickly on the emaill reports.
better solution IMO is cheap credit monitoring, something like each credit reporting company sells. You can always work with your card holders too and take their advice but just beware closing down a card and then re-opening it, if they do it wrong you'll lose credit for all the history you have on the account. Credit scoring is a bit more complicated than a lot of places tell you. You have no choice if a card is lost or stolen many times but if the company you're working with really cares IMO their customer service should put the new card on your report correctly ie put back all the time rated on it.
If you just cancel one and open a new one incorrectly it looks like a brand new card if done wrong which can impact your score.
I recommend reading this
That last one length of account is what I was talking about when one is canceled and replaced.
This monitoring also comes with a free credit report every so often so you can pull one on yourself and review it to make sure that you're the only one using them and they're all ones you've opened.
Your credit score affects more than you think, It can affect insurance car and home owners and of course any loans you might get.
Chances are someone you swiped your card or gave it to way back whenever is who might have done the probing or sold it to someone who did, if one more card starts doing funky things then I'd say you have a more serious problem but the monitoring will usually catch this fast enough you can alert your card holders.
Try to avoid using a wirelessly connected computer to input your credit information over, don't let people get out of your sight with a card, make sure they give it back quickly, CELL PHONES HAVE GREAT CAMERAS NOWDAYS.
Hope this helps.