No you can make payments without, simply by clicking on " Don't have a PayPal account? Click here " , when you see the PayPal login screen.
Then fill in your credit card detail as per normal.

We would however recommend it, as that way we have your contact details, should anything go wrong with your order.
You will also be able to use it again at a growing number of site, and thus avoid telling too many people your credit card details.