Today I tried to buy a game and pay for it using Paypal but I couldn't because Paypal asked to add a Credit Card to my account or transaction can't be finalized.

I know that some sites require Paypal account with added credit card to it but on GOG I never had this problem. Something has been changed in this matter? Can I buy a game on GOG without credit card?

Yes you can, but you need to be able to pay 'directly'.
I'm assuming you have linked your bank account to Paypal, sometimes Paypal just changes the status from 'direct' payment to 'delayed' payment when you use a bank account.
Same thing has happened to me several times.
You can fix it by either doing a delayed payment to a website that allows this, such as Gamersgate or DealExtreme, transferring money to Paypal or by using a creditcard.

Thanks, I realized that I hadn't enough money on my PayPal account. They should told me "You have no enough money on your account" instead "Please add your Credit Card". It was kinda misleading.

Yep it is.
And their customer service SUCKS.
They make even GOG look good.

Heresy!!!!

GOG's customer service is awesome. Best ive had.

*tiny little writing below*
Except YuPlay who still refuse to provide a full download.>.<