I never travel internationally without full travel insurance, including unlimited medical and collision damage for hired cars. For internal travel, I sometimes just buy the airline's cancellation insurance, depends on the circumstances.
If you'll be hiring a car for any length of time, the collision damage waiver often costs more than a full insurance policy that includes collision damage. Check the waiver costs before you travel - they're not usually prominently displayed on the website/advertising. For one or two days it's not a big cost but for a week or more it often comes to an outrageous amount.
One other point - it's a good idea if everybody in your party is on the same policy. When I was on a holiday with a friend and her son, my friend became ill. She had said she wasn't going to get travel insurance as it was too expensive, but I told her I wouldn't travel with her unless she did, so she got it and was glad she had it! Anyway my policy wouldn't cover any deviations for me to care for her or her son, since we weren't on the same policy. She was way too sick to look after her son, and I was worried how she'd manage on the flight home. I managed to send her son back home unaccompanied to his Dad so at least we didn't need to worry about him, and then it was a bit tense seeing if she'd be discharged from hospital in time for me to help her on the flight home. I ended up missing one flight and out of pocket by about $200, then we made the connecting flight OK as we'd had an overnight layover on our original itinerary.