I've always been upset that hotels ask me for my passport when traveling outside of the US. On my last trip to Thailand and Singapore I tried to refuse to give them my passport but they insisted. I had one night in a inexpensive no-frills 1.5 star hotel and even they needed one. Two of the hotels photocopied my passport.

I understand the need for renting a car as you're borrowing a $10,000+ item from them. It is a matter of policy at most (if not all) car rental companies to take a copy of a passport and applicable drivers license for all people that don't have a USA drivers license.