To begin with, I have been using various credit cards for online purchases since 1999. I have NOT had any problem(except on one occasion) as I have been dealing with well known foreign sites such as Amazon and other major booksellers.
However-you should follow these precautions:
Use only sites with security settings(https) and the lock symbol
Avoid anything dubious(especially pornography)
Avoid any private Indian site.
Railways and some airlines(Air Deccan, Jet) are safe enough.
But there are plenty of complaints against the "shopping portals", particularly when things are not delivered. If you must deal with such parties, make sure that there is a physical location near you where you can personally go to complain.
The only problem I have had is when books ordered from abroad and sent by unregistered mail did not arrive. Generally the foreign sellers refund your money promptly in such cases. The only bad experience I had was with Barnes and Noble of USA who never responded to my complaint. Apart from this, I have had no problem about complaint resolution with Amazon and other foreign sellers