While having the receipts for your purchases is the preferred method of proving you owned items that have been stolen or destroyed, there are other methods that will work as well. The best idea might be to call your insurance agent and ask them what sort of proof of ownership is accepted, but here a few tips of ways to avoid the problem as well as workarounds that will provide proof of ownership in different ways.
Canceled checks and credit card statements that show the purchase amount is usually acceptable in lieu of having the actual receipts. Similarly, a warranty card or owner's manual for the products will usually work as well. Since it is difficult to have an owner's manual if you didn't own the product, and useless to own a warranty for something that does not belong to you, these two forms of proof work well, especially when used in conjunction with something like a home inventory.
A home inventory is a record of the possessions in your home. Keep in mind, though, that the home inventory will not help much unless it is both kept current and you have filed a copy with your home insurance company. The best way to take a home inventory is to use a video recorder and go from room to room recording everything in the room. Do not forget to video the contents of your closets, your furniture and appliance, and anything else contained in the closets, cabinets, and other storage places.