Hotel safes are no Ft. Knox
The video below demonstrates how easily a trained safe-cracker can pick open some models of room safes. Most of these safes are also not made to withstand heavy-duty assault, so if criminals have reason to believe you're storing something of great value, they might overwhelm the safe with power tools. Another risk comes from today's micro-cameras and wireless links, through which a thief could look over your shoulder as you key in the safe's pass code.
Also, since guests routinely forget the security codes they've set in their room safes, the hotel will have an alternate way to access that safe. Just how secure is that information?
Lastly, you should understand that hotels put limits, sometimes absurdly low, on their liability if something is stolen from the room's locked safe, and documentation will be required to substantiate a claim.
None of the above is meant to dissuade you from using your hotel room safe if the only other options are leaving them loose in your room or carrying them with you into perilous situations. Just don't underestimate your risk, and when packing for a trip, bring only the treasures you really need.
I'd also consider the suggestion of AARP"s Peter Greenberg, that you consider adding a diversion safe to your travel kit.