Sometimes yes and sometimes no.
It all depends on the insurance company but most times your homeowners insurance monthly cost will increase by $50.00 to $100.00 per month should the insurance company discover you have a trampoline on your property.
Trampolines are likely to attract neighbors kids to your home if you allow neighbors kids on the trampoline and when they get hurt your insurance may need to cover the cost of any injuries to the kids or person who used the trampoline.