I am one of those sleazy insurance guys. It really depends on the company. Different insurers have different individual item limits that they will pay without items having to be scheduled. You really have two options. Schedule any individual game that is above that individual limit your insurance company will cover on a separate endorsement or as was mentioned in a previous post here, you can look for an individual collectors policy.

One thing you should do regardless of which way you go, is to take updated pictures of your collection anytime you change something just as proof of what you had in your collection at that time.