Google Checkout is now Google Wallet, a service like Paypal.
Indian cards, when used online, have lots of restrictions, redirections, verifications etc. The catch is, everything must happen in real-time; making it impossible to be used in services like Google Wallet where Google stores your card info and uses it at some point in future.
Previously, Google Checkout was real-time, so some cards used to work. Blame Google for making another Google+-esq mistake by removing any direct payment method with the aim of pushing its Google Wallet as a major competitor of Paypal.
I contacted their support, they said that SBI debit cards shall work. However, Saketme reports that even that is not working. I request him to contact Wallet support and post the response here.
Update: Some say that these cards stopped working because INR transactions have been implemented. Axis Bank cards used to work, so did virtual credit cards; both are now bocked.
Edit: Can I post links? thinkdigit.com/forum/internet-www/161111-must-read-information-regarding-indian-debit-cards-8.html