With the potential liability home inspectors have, it's a no-brainer that you need E&O insurance. This protects you from the crippling costs that a lawsuit can bring with defense costs, damages and loss of assets.
A quick Google search turns up the $600-$1200/yr range for a basic E&O policy (source: Coverwallet)
This map from Elite MGA shows you how much you might need in your state. Some states require it and some don't so be sure to check. If your state doesn't require it, it's generally advised that you have some level of coverage.