Hedging events with poor or no insurance penetration. For instance, suppose you had to pre-pay in advance for a venue for Spanish soccer finals game party before you know if they go to finals, you might hedge your position by betting against them going to the finals, especially if the chance was very high as a small premium would protect you against a total loss.

Another common one is war. Most insurances don't cover acts of war. Getting underwriting can be difficult especially for smaller amounts / people with little access to finance industry. Betting on war can hedge real estate or other exposed holdings.