When we get to our hotel, the passports, extra credit cards, health cards, traveller's cheques etc. all go into the safe and the key goes on my car key ring. I always carry my keys in my right pocket every day of the year, so I realize very quickly if I've left them behind. The only time I'm apprehensive is when we're all going swimming. I then hide all the keys somewhere in our room. I also have photocopies of my passports and traveller's cheques in my van in case someone does get in and break into the safe.
I'd rather risk leaving them locked up in the room then carrying them around with me from park to park. I think the chances of a burglar choosing your room out of the hundreds to choose from is pretty slim.
I also leave the same photocopies at home here with my Mom. I hope that I never have to make use of the photocopies.
The safes at BCV, CR, and OKW are huge. We also leave one of our cell phones in their as well.