Do I still need insurance?

So, my house is fully paid off. I recently got a large inheritance, much more than my house is worth. I'm wondering if I still need to pay for the insurance that I got when I had a mortgage. I figure that in the slim chance that something bad happens, I could cover it myself. Should I keep paying for it, or save the money for other things, and keep a bit of the inheritance money aside just in case something bad happens?