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 ?
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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.