When I try to install Steam (on Ubuntu 13.04) from the Software Center, it asks for payment details even though it is free.
Can I install it without a credit card ?
Go to steam, download installer and doubleclick. You can now get back to software center and install without logging into Ubuntu One.
While the only option is to click "Buy", you only have to sign into Ubuntu One without paying anything. As you can see, Steam is flagged as a "Free" software.
Once you are logged in, the Software Center will tell you that it's "checking your payment information", but don't worry, it won't charge you for anything. Actually, I don't even have any payment information on my Ubuntu One account.
After that, you'll have to enter your admin password and you'll be good to go.