I've got a sizable renter's insurance policy in case of emergency, and everything I own is well documented.
I've thought a lot about this though - in the event of an emergency, how the hell would you convince an insurance company that a bunch of old games are worth north of $10,000? I could see that being a major issue.
My renters insurance does not cover collectibles, so you may have a problem if yours is the same. My renters insurance does cover the replacement value of "video games," and in discussing it with the insurance agent this is kind of a flat rate per video game. You should give your agent a call for peace of mind sake.
In my experience anyone that has had lost stuff due to flooding, fire, theft, etc. is always screwed by the insurance company. I expect that I will be able to get some $ back, but realistically, I do not believe it would be near the replacement value.
At the end of the day, I agree with the Professor's assessment. Wife/gf/family doesn't need to know about something they don't quite understand, but do your best to explain in a will. While you are alive you don't want the games causing any conflict. When you are dead hopefully the will takes care of everything, but if not, you're dead...