Do hotels keep your passports?

You were told the wrong thing.
They never keep your passport that you need to show when they check you in.
They just record the information on it.
It is just like check in the USA where you have to show some ID and they give it back to you.

If they want to see your passport, they will want to see your actual passport, not a copy.

Most hotels copy what information they need and then return your passport immediately.

You are required by law in Italy to register with the police. Rather than having thousands of people go to the police station every day, the hotels do it for you.

They used to keep your passport to copy later but most now just take a photocopy of it. Some may still hold it but you can usually retrieve it within a short time.

You need to give them the original.

Keeping your passport happens a lot less frequently than it used to since they mostly just scan, photocopy, etc. at the desk. But it has happened to us in a couple of Italian smaller hotels in the last year, so it is still possible. I wouldn't worry about it though - but do remember to pick it up later since it's annoying to arrive in Venice and then recall you left your passport with an hotel in Milan.

In my experience the passport may be held for awhile if the front desk is very busy when you check in or if you are staying at a small lodging place that doesn't have a photocopier near the front desk.

If you are asked for ID at home, what do you show?
When you are outside your own country, your passport is your ID, that is what a passport is for. You may need to show your passport as ID in many situations, and hotel check-in is one. They are required by law to record the ID, including passport details, of all foreigners. And they must see the original, copies are too easy to fake.
In the old days they kept them, until they had a few minutes to write down the details, then handed them back in the morning. Nowadays they copy or scan them, unless they are busy then they keep them until they have free time.

Think of your passport the same as you do your ID at home, it is an everyday thing, it is not "gold plated".

In my experience the passport may be held for awhile if the front desk
is very busy when you check in or if you are staying at a small
lodging place that doesn't have a photocopier near the front desk.

Gina, this has been our experience as well, and it's completely normal. If they're too busy to photocopy or take down the necessary info on the spot, they'll send us to get settled in our room first and have them ready for pickup when heading out for sightseeing, dinner, etc. Nothing to worry about.

Before the days of computers, photocopiers, and scanners, it was not uncommon for a hotel to keep your passport for up to a few hours to get the needed information, especially if it was busy. As stated, now they are most frequently returned within a couple minutes.

I also remember the days, many years ago, where your passport, in very small hotels/pensions, was kept until checkout, basically as collateral until you payed the bill. But regardless, no harm in leaving your passport with them for a few hours.

It is fairly common for museums and expositions to ask an ID or passport when renting audioguides, and the ID card is returned at the end when the audioguide comes back.

....I was told that hotels at check in, take your passports? ...... I suppose it is how you define "take." But it is common in Italy to "take" the passport and go to another room to copy it or copy it right there. Within the passed year we stayed in a small hotel that asked for the passport, took them without any comment, and handed us the keys. Later that afternoon when we return the passports where in our key slot and were given to us along with the room key. By the way, it is more common and actually expected for you to turn in your room key when you leave the hotel. It is their way of doing business and it doesn't have to make the American way of doing business. Don't get uptight with different procedures.

Just to give you a head's up, I had stayed at an AirB&B in the Cinque Terre where the owner did take our passport and returned it the very next morning. I was quite alarmed, but all was well. Perhaps this was because she had less technology at her finger tips and needed time to record? Otherwise, anywhere else I only had to show it.

The hotels used to keep the passports longer. Nothing to worry about. They are required to request your passport by law.

I agree with Chris, that's what your passport is for, it's your id outside your country, so airports, hotels, police, maybe even museums can ask you for it. There's nothing special or secret in your passport, just name, date and place of birth, so it's not really secret information...

By the way, it is more common and actually expected for you to turn in
your room key when you leave the hotel. It is their way of doing
business

We haven't always been requested to do that but another little hint is that if your room key is a card, it sometimes also activates the lights in the room. There will be a device on the wall, usually near the inside of the door, that you slide it into. When you leave, you remove it. As electricity is expensive there, it's a way of ensuring that lights and whatnot are out when the room isn't occupied.

Thank you all for your responses. After all, this is what this forum is for to ask questions and discuss our trips. However, this is for Chris F. from Switzerland. Perhaps it is because I am American and you are from Switzerland and may not understand your exact tone. I fully know what to do with an ID and have no problem giving someone my passport for information in a hotel or anywhere. What I was asking is if the hotels take and keep the passports for the duration of your stay. I'm aware it is not gold plated and as no secret information on it. But if they did keep it, yes, I would feel uncomfortable going out for the day, without my identification on me. I think that is just being responsible in another country. I now understand how it works thanks to the polite responses.