Until a few years ago the insurance industry in India consisted only of public sector companies: Life Insurance Corporation (LIC) was the only company selling life insurance policies and there were four public sector firms selling general insurance products like medical, householder's and vehicle insurance policies.
Mediclaim is the brand name of the medical insurance policy offered by public sector general insurance firms, but it is widely used generically, even in the Press, to refer to policies sold by the private companies as well.
Likewise, xerox (from Xerox Corporation, manufacturer of photocopiers) is used both as a noun and as a verb to mean (to) photocopy. And the popularity of the Hoover vacuum cleaner in the US led to it being used as a verb: to hoover, meaning to vacuum.
Do you know of any other brand names being used generically?