Nobody is going to steal your identity, relax! :-)
For good measure you should tuck a few copies of your passport away in your luggage/backpack anyways.
Here is the deal:
Europeans, and visiting foreigners are required to register their residency, even be it for a night.
In America I constantly had to show my drivers-license for ID, in Europe it's the passport:
almost all Europeans have a passport (but few have driver licenses),
so, it simply is the ID of choice, especially for foreigners visiting. It's really nothing to worry about!
I know that only about 24% of Americans own a passport, so I can understand why it would be upsetting to you to have to hand it over -
but!!!!!!!!!!!
These days,
as already posted,
it involves no more than getting it copied, or knowing your passport number, and filling it in on your guest registration form the next morning over coffee and crisp rolls/croissants :-))
I have my passport number written down in my journal, for just such occasions.
Granted, I am European - but I haven't been asked to actually hand over, never mind show, my passport at reception, for YEARS!
Enjoy Europe, everything is very relaxed here - we have open borders AND open hearts.
So come on over :-))