I have traveled to 56 countries (so far!). I use TSA approved locks all the time and have never yet had one cut off. For all the rest of the world you can use any type of lock that you want to, but I still use the TSA locks, because that is what I have. I always carry a spare lock in my hand babbage, just in case one is cut off, but have not had to use it yet.

My experience has been that most countries screen your luggage before check-in, while you are still present (and so could open your own bag, if this is deemed necessary). Only once (in China) did my baggage need to be opened when I was not present. The airport called for me on the public address system and I then opened my own bag for the Chinese airport security screeners.

From what I have gathered, it is only in the US that they cut your locks off!