Nothing has ever been safe. If you walk into the place of business with cash to pay a bill, there's nothing saying the person you hand the cash to won't just pocket it. Send a check, there's nothing saying the wrong person won't cash it (I am personally aware of instances where companies have cashed checks made out to former employees), credit card numbers can be (and have been) stolen. Things like PayPal, for all their hype about security are probably less secure than a credit card, just because they're tied directly to a bank account.
All in all, credit cards are probably the most secure method of payment. You can dispute charges, they are quite vigilant about watching for suspicious activity, and at least in the US, you're only responsible for like the first $50 of fraudulent charges. Which was probably a lot more money when that particular regulation went into place.
Still, it doesn't really matter how secure things are on your end if someone just breaks into the merchant's systems. If you do business with a company that stores all credit card info in plain text, no encryption, and doesn't really bother properly securing their back end systems, I don't care if you have a quantum entangled communication system which is impossible to intercept, your data is still at risk. I think of it kind of like a Red vs. Blue episode... One guy asks a soldier to open the gate to his base. The soldier says, "Sorry, no can do! See this here is a secure facility!" The guy responds with, "Then I guess we'll just have to go through the giant hole in the wall of your secure facility." And the camera pans over to show a huge section of the wall has collapsed.