Absolutely yes, it is possible for people to travel the world and stay safe. But for safety point of view you should follow some safety rules because while travelling lots of problems you may face- like language, money etc.
Therefore with enjoyment of any trip safety should be your first priority. There are some safety rules which make your trip safe and healthy
Before your trip research your destination.
What type of destination you have selected?
Is it safe or not according to your budget?
If it is an adventurous trip then what are the risk?
Is your travel agency covering your insurance policy?
What types of dressing are there which makes you comfortable in your destination?
Your valuables with you all the time because while travelling it is very risky to trust other. So please don’t you ever trust anybody in unknown city. Check your drink every time.
It doesn’t mean that you don’t make friendship with strangers. Making friendship while travelling is to be quite good experience, but don’t trust people too quickly
Keep your important document and some secret cash separately. In any worst case it will help you.