Do credit cards generally cover all needed insurance for rental cars?

I'm thinking of changing my basic visa card to one that offers collision insurance for rentals. Would that mean I can get a car without any other insurance add-ons, or will I get to the rental place and the guy will convince me that I also need x, y and z insurance, and if I rely only on the insurance my card gives me, I'll be taking my financial life into my own hands?