It depends on the country, the hotel, and the nationality of the guest.

As an EU resident, I've never been required to present a passport in any of the EU countries (or new incumbents before 1st May), the US, Canada, Aus, NZ, Malaysia, Thailand and others, but am inconsistently asked for my passport number on the check-in form.

To be honest, I do it that often now, I just memorise my passport number - it's only . Saves ferreting around for it.