Note that the typical gamer's collection is not "collectible." This is recently purchased stuff for the most part. That falls under "contents" of the house. A typical HO policy (for a homeowner) or an apartment dwellers policy have a Contents limit. This means that if a fire destroys your stuff, the appraiser comes out and finds the value of the stuff. They pay up to the Contents limit for the
actual cash value. That means what it's worth on the street. Typically there is depreciation. There is also a deductible. (If you have a very minor loss it's often not worth it to collect because premium goes up.)
Deluxe homeowner's policies pay replacement cost. This is whatever it takes to get new stuff (less deductible). Find out what kind of policy you have and if it's ACV, pay for replacement.
If you have a large collection of books, then they may be collectible. At this point your insurance agent is the person to talk to. It's still Contents, but it is typically excluded if they are "rare". However, this depends on the policy. If your agent says its covered even after you ask this question, get them to put it in writing. You should receive a copy of your policy when you sign up for insurance. Read it and ask what stuff means.
A Valuable Papers policy or Collectible policy typically require a value to be placed on the collection, which means an appraisal. This is tricky. I don't know of any experts on gaming collections. The insurance company might go to a store owner or use the Internet. Always inventory the collection including photos. Keep the inventory on computer and make a backup CD to store at work or in your car or at a friend or parent's house. Remember to update it at least once a year.
The issue with collectible policies is that the premium can be as much as 10% of the value of the collection. So in 10 years you paid for the collection twice unless you get an excellent quote.
I am not a lawyer. This is not legal advice. I do work in the insurance industry. Good luck!