It's important to keep your passport with you when traveling abroad,
with a few exceptions:
. A hotel clerk may ask to keep your passport for several hours or
even overnight in countries where foreign visitors must be reported to the
police. (This is a common requirement, even in Western Europe.)
. Occasionally, a bank clerk may need to borrow your passport for a few
minutes to complete the paperwork for an exchange transaction. The teller
will return your passport when handing over your cash.
. If you need a visa for the next leg of your trip and didn't obtain it at
home, you may be asked to leave your passport with the consulate that's
issuing the visa.
Are you the type of person who misplaces things, or are you worried about
pickpockets? Buy a "neck safe" or passport/money holder that can be worn
inside your clothing.
IMPORTANT:
. Don't lose your passport under any circumstances! Without it, you'll
be limited in what you can do and you'll waste much of your
vacation trying to get it replaced.
. To minimize bureaucratic difficulties if your passport is lost or
stolen, carry a photocopy of your passport's photo and identity pages in a
safe place. This way, you'll be able to prove who you are when you apply
for a replacement at your country's embassy or consulate.
source: Europe for visitors.