I often use the hotel safe for my laptop and valuables, though we rarely take any significant valuables. I prefer to keep my passport and credit cards with me but that is not because I don't trust hotel safes.
We had an interesting thing happen last summer in Saipan. We went to open the safe and it was dead. We were heading out for the evening so we stopped at the front desk and asked engineering to come and fix it while we were gone. They were NOT keen on opening the safe without us present but eventually agreed. So kudos to them I guess. When we returned it was working with the combination we had originally set. I'm pretty sure they just replaced the batteries but have no idea how they opened it with the electronics dead. So I'm suspicious there might be a mechanical release somehow, possibly activated with a tool from outside but I have no idea.
I tend to prefer nicer hotels, 4 star, so I tend to think they have decent security anywhere in the world. Although, living in Hawaii I have met a few people who worked security at 4-5 star resorts and man do they have stories to tell about guests. Let's just say murders, suicides, and domestic violence are far more common here than you might think and are rarely reported in the news media. But theft, other than petty theft of things in the pool area, is actually not common here. Of course it could be very common elsewhere.