For European residents, compulsory insurance (i.e. 3rd party liability) is almost always included in rental rates. It's pretty much unheard of to have credit card or domestic motor insurance covering rentals.

For US residents, it depends on where you booked and how. The majority of bookings will include insurance, but some of the majors will effectively allow you to 'opt out' if you are a US resident (and allow you to use your own insurance). This is not always transparent, so it pays to check the small print.

CDW and TW are typically also included, with a sizeable excess (which you can pay to reduce).