Interestingly I have a different perspective than @ShutterBug. I live in a safe country but travel often to ones that are not.

The main difference is that I do not blend in with locals. That means no amount of being inconspicuous, hiding company logos, etc will put me out of sight. Everyone nearly instantly knows that I am there. I've been followed and approached by friendly curious, unfriendly, aggressive and dangerous people.

Avoiding lone journeys is good advice and applies everywhere. I know that 2 people together are 10 times more safe than one. You cannot always be in a group, particularly for early morning and evening shoots. I have used a police escort in several countries, sometimes they do it for free, sometimes there is a fee and sometimes a tip will do.

Public transport is very dangerous in many countries. I've been to places where the bus driver watches while someone gets assaulted in the back of the bus and he continues his job as usual to avoid problems for him. I've been always recommended to use official taxis. They may cost twice as much as others but are worth it. You can usually get those from hotels, high-end restaurants and important business areas. They should have a traceable number and clear identification. If you are worried, use a cell to SMS the identification to an email address.

A shot only matters if you can bring it back. Shoot when you have too, unless you cannot do it safely.

When asked, pay bribes quickly and move on. It's sad to have to do that but away from home, it can be much more problematic not to.

My experience is that most danger tends to be concentrated around high population centers. Also in outside areas of tourist interest, national park trails, known vista points, etc. In rural areas, there are usually less danger and people are more friendly and willing to help.

Disclaimer: I've only been to 47 countries, so I may be wrong about the other 146.

EDIT: Just realized I did not answer the first part of your question:

I pack my gear in a shoulder bag. It is a regular camera bag and I do not think what it looks like matter because the moment I take a picture, people know there is a camera in there. The most important is that I wear it across my body and always in front of me where I can see it.

All my gear for a shoot fits in that single bag and I don't let it away from me anywhere. Backup gear remains in the hotel in a hard suitcase tied up to a permanent fixture with a special cable and lock. As much as possible, the primary and backup gear bags are kept separate.