Once you own the home 'free and clear', you do not have to have home owners insurance on it - but why wouldn't you? What is something happens to the house (i.e. burns down). Do you have the money to pay for replacing it and everything in it?
If it is paid off, the lender's lien is satisfied and, thus, the requirement for hazard insurance. My personal practice is to carry insurance on anything I do not have ready funds to replace. So, if I could not afford to rebuild my home after a fire, for instance, I would still maintain hazard insurance.
No. But unless you have money to burn, (pardon the pun) anyone owning a home and not insuring it has rocks in their head! It's not just physical damage you need to protect your wallet against, but the potential liability and/or possible lawsuit against you should anyone get hurt on your property.
Once your home is paid for there is no legal requirement to carry insurance, however unless you're basically well heeled enough to "self-insure" I would highly suggest that you do maintain insurance on your property. If you work with a financial adviser you could always ask them for their opinion as well.
Remember not only does it cover repairing/replacing your property in case it's damaged, but it offers you liability coverage in case someone were to get hurt on the property. It also enables you to pick up an umbrella policy which offers you even more liability insurance very inexpensively which is unavailable to non homeowners.
Once you own your home free and clear there isn't a lender requirement to carry home insurance, but it is certainly recommended. Homeowner's insurance can protect you against many things, possibly even provide protection if someone injures themselves on your property.
The great part about the lender requirement being removed is you have a lot more flexibility. I would suggest meeting with an insurance agent and deciding what coverage you need or want and deciding from there. I'm happy to supply you with a referral if you like.