I was very lucky and got all my stolen stuff replaced through the insurance company. My friend wasn't so lucky - same company, but a student policy and they ripped her off and gave her a shocking amount of hassle. I've now started an inventory of books and cds, and keep photocopies of receipts for electrical goods.
It is quite amazing what lengths insurance companies will go to in order to avoid paying out. They'll try and get you off your books if you're so much as a second late with a payment. (I worked as a programmer for a certain big American insurance company and I hope never to have to deal with commercial auto cover again!)