Having travelled a lot in developing countries, I am always aware of camera security. I know of people who have been followed from the airport and had all their luggage stolen from them immediately before entering their hotel. I also know of people who have lost their cameras in the street. It is sensible to organise your travel from the airport to the hotel prior to arriving and plan all your routes and travel methods. There is nothing worse than being robbed while on holidays and needing to organise cancelling credit cards, etc from a foreign country I have had this unpleasant task once while in Bogota.
There is often nothing you can do to blend in however, you can make an effort not to stand out too much. I try and dress down when travelling and not to carry too much luggage. While on the street, I keep my camera bag in front of me and with a small lanyard clipped to my belt. I normally return my camera to its bag or tuck it under my coat.
I once had an experience of an attempted theft in Buenos Aires in the centre of the city. A boy jumped off a bike, that another was riding, and approached fast with the obvious aim of getting my camera - with the noise he made and my wife noticing him I turned to face him and he changed his course and jumped back on the bike. Shortly after, we saw the duo caught by the police. Expensive cameras are offered for cheap prices in many city centres, obviously stolen, so the risk is real.
I use the safe in hotel rooms, when my camera fits or if heading out for a short time without it use the "do not disturb" sign. A Pelican case is a good option and can be chained to the toilet that is often a good place to use.
When travelling by car I try not to ever leave gear visible through windows. I know of a number of people who have lost camera gear while travelling or from their camera in front of their house. Again plan your travel carefully and your internal travel.
Also when in secluded places be aware of the risk of theft – dark alleys are not always the most sensible places to shoot alone!
There are many blogs on carryon versus check-in of camera gear on planes. I have not ever had to check in gear but never carry that much. I have however had stuff stolen from my check-in so that risk is obviously real too.
The lesson over the years for me is to pre-plan, blend in where possible, and stay aware of your surroundings but not to let is stop you photographing unless it really is not safe!