The answer, in many places, is yes.
Sometimes hotels may legally demand that you hand over your passport when you check in.
"In some countries, hotels may be required under local law to retain copies of guests' passport information," a U.S. State Department spokesperson confirmed with me.
But that doesn't mean you shouldn't take additional steps to protect your documents.
The details of how your passport will be handled vary depending on the location. Some local or national governments require hotels to record the passport number and name of every foreign guest, and that information might have to be submitted to local authorities.
In the European Union, member states are technically required to validate your identity through your passport upon check-in. In the United Kingdom, a law established a half century ago requires hotels to record the name and nationality of every guest over the age of 16, and to retain that information for a year.
Most of the time, hotels can record the proper details when you check in, but in other places, complying with regulations can be more complex, requiring hotel clerks to retain your passport for a while.
However your information is recorded, though, the paperwork usually doesn't take long to complete, so in many places, it will be reasonable to ask for your passport back after a few hours or overnight.
Some hotels, though, will ask to keep guests' passports secure for the duration of their stay. Sometimes it's because of a stringent local mandate, but sometimes, particularly in low-cost accommodations—and this is where the demand enters a gray area—it's because the manager wants to ensure you won't skip out on your bill.
Some cruise ships, too, particularly small ones, may ask to hold onto your passport for the duration of your vacation so crew may validate arrivals in each port without having to disturb guests.
Unfortunately, most tourists don't know the regulations in the destination they're visiting, which can put them at risk of surrendering their passports for the wrong reasons.
"We encourage U.S. citizens to research their hotel for any such requirements and safeguard their important documents while traveling," the State Department advised.
Passports are technically the property of the government that issues them, but officials still place the burden of keeping track of them on the traveler.
You can do a few additional things to be prepared for any situation.
Carry photocopies of your passport profile page.
Some hotels will accept a clear copy of your passport page as long as you can prove that it's identical to the original.
Even if the manager won't oblige and insists upon keeping the genuine article, you can always carry the copy with you as you explore the destination.
Do not write your home address in your passport.
If you're worried about identity theft, rest assured that it's rare for hotels to use your passport to take advantage of your details. It's bad for business.
Make things harder for impostors. Think twice about listing your residence in your passport. After all, everyone who handles your documents in the hotel office will know for a fact that you're not at home.
If you're concerned about losing your passport, stick with writing phone numbers and email addresses that can't be used to falsify your identity.
Ask the hotel clerk to teach you the following phrase in the local language: "My passport is at the hotel."
That phrase can come in handy if your passport is requested while you're out and about. If you're in a destination where hotels traditionally retain passports, locals will be used to the concept of visitors not carrying the documents.
Should something go wrong despite your attempts to mitigate the risk, the U.S. State Department can help Americans deal with the aftermath. "We publish guidance on our website for U.S. citizens on how to get assistance in the event that their U.S. passport is lost or stolen abroad," the State Department spokesperson said.
The government of Canada provides similar services through its official website, as does the United Kingdom (at Gov.UK), the government of Australia, and pretty much every big country. Before leaving home, learn where to find help for lost or stolen passports from your own home government.