My view is from the Netherlands, a EU country.
Con: Credit cards are more risky.
If someone finds your card, they can use it for online purchases without knowing any PIN, just by entering the card number, expiration date, and security code on the back. Worse, sometimes that information is stored in databases, and those get stolen by hackers!
Also, you can have agreed to do periodic payments on some website and forgot about them, stopped using the service, and be surprised about the charge later.
Debit cards usually need some kind of device that requires your PIN to do online payments (the ones I have in the Netherlands do, anyway), and automated periodic payments are authorized at your bank where you can get an overview of the currently active ones.
Con: Banks get a percentage of each credit card payment.
Unlike debit cards where companies usually pay a tiny fixed fee for each transaction (of, say, half a cent), credit card payments usually cost them a percentage and it comes to much more, a significant part of the profit margin. I feel this is just wrong.
Con: automatic monthly payment can come at an unexpected moment
With debit cards, the amount is withdrawn immediately and if the money isn't there, you get an error message allowing you to pay some other way (credit card after all, other bank account, cash, etc). When a recent monthly payment from
my credit card was due to be charged from my bank account recently, someone else
had been paid from it earlier that day and the money wasn't there. So I had to pay interest, on something I bought weeks ago...
Pro: Credit cards apparently have some kind of insurance.
I've never used this and don't know how it works, but apparently you can get your money back easily after fraudulent charges.
Pro: Credit cards can be more easily used internationally for online purchases
I don't know how it is with Visa or MC-issued debit cards, but many US sites accept only cards that have number/expiration date/security code and thus my normal bank account debit card isn't useable.
Conclusion: definitely have one, but only use it when absolutely necessary.