You can allow your customers to choose whether or not to save a new credit card on checkout.
Settings > Orders > General > Checkout Settings
If 'Enable One-time CC For Logged in Customers' is enabled, logged in customers will be given the option to save their credit card information to their account during checkout when entering a new card. Note: If this option is disabled, all new cards will be automatically saved.
The 'Save New CC By Default For Logged In Customers' setting will determine the default state of the checkbox that determines whether or not to save the card. Note: This setting is only applicable if 'Enable One-time CC For Logged in Customers' is enabled.
On One Page checkout, this is what logged in users will see if you have these settings enabled:
For this to display correctly, you may need to add the appropriate visibility area onto your One Page Checkout theme html. Themes > Edit > One Page Checkout > Html Editor
The visibility area that powers this is called 'CreditCardSaveArea'. The merge code to render the checkbox and label is $$SAVECARDCHECKBOX$$
Note: If you want to change the text that is rendered with the checkbox, it is in a store text key called 'OnePageCheckout_SaveCardCheck_string'