Do hotels have insurance for their customers' items?
I've seen signs in hotels that say the business is not responsible for lost or stolen items. Is that because they can't buy insurance for their customers' stuff?
In the insurance industry, there is a general principle which states that one can only buy insurance on things they have an insurable interest or financial stake in. For example, I cannot buy an insurance policy on your house and receive payment if it burns down because I do not have any financial interest in your house. However, if I had lent you some money to buy the house, I could be asked to be put on your policy as a loss payee and receive payment if the house was burnt down. This is because, as a lender, I would have some insurable interest in your house equal to the portion I own.
With that being said, there are also some situations where I could have no actual financial interest in your property but could still insure it. Bailee's liability insurance is a good example of this. A bailee is someone who has custody of another person's goods for purposes other than sale. For example, if I ran a watch repair shop, the watch you left with me could be insured under my bailee's liability policy. (There are several different types of bailee's liability insurance policies, but that is a conversation for another day.)
Translating this principle to the case of a hotel, hotels can act as bailees for their customer's property and can therefore be held responsible for the safekeeping of that property. If the hotel acted negligently and fails to adequately protect customer property left in their care, they may be liable for the loss or theft.
To protect against this, most hotels purchase something called innkeepers legal liability insurance that will pay up to the amount required by local laws. Usually up to $1,000 per guest (see Running a Hospitality Business? Here's the Insurance You Need for more coverage hotels need).
Laws regarding innkeeper liability varies from jurisdiction to jurisdiction, but despite those signs claiming no responsibility for lost or stolen goods, most hotels do carry some sort of liability insurance that covers damage, loss, or theft of customer property while on premises and in the custody or control of the hotel.