CE Magento supports subscription based sites using what Varien calls Recurring Profiles. While they only support Paypal by default, you can purchase extensions

CE Magento supports subscription based sites using what Varien calls Recurring Profiles. While they only support Paypal by default, you can purchase extensions from a variety of different companies to handle recurring profiles in Magento. We choose the Authorize.NET CIM route. Others may choose to use Braintree. Both have extensions to support recurring profiles in Magento. The trick is to figure out how they work, there is little to no documentation on the process and most of it will involving setting up a good DEV environment/staging etc.