Probate is required when an individual dies with assets in their name only, and that don't automatically transfer to someone else. Examples include individual bank accounts, cars, investments, etc.
Jointly held assets that have Rights of Survivor aren't subject to Probate as they automatically become the surviving joint owner's property.
Assets with a Beneficiary Designation (life insurance policies, retirement accounts) also aren't subject to Probate as long as there is a valid living Beneficiary.
Assets held in a Trust do not need to go through probate.