Even if Armenia is one of the safest destinations in the Caucasus , you will still need to be vigilant, particularly in sensitive areas of the country.
Even if you don't feel at risk during your trip to Armenia, you should (without becoming paranoid), remember that you're in a poor country where pickpockets exist and attacks may occur. Problems are more likely to arise in touristy areas, on public transport, in certain neighbourhoods that you should avoid and once night falls.
Some people find themselves being tempted by drug dealers, leaving them in the midst of more unsavoury members of the population.
You should also bear in mind that Armenia has certain zones that could present a security risk. These include areas that border Turkey and Azerbaijan as well as the Nagorno-Karabakh enclave. Warning - landmines ares still found in this part of the country!
To avoid being a victim of theft, the best approach is to not draw attention to yourself. Don't flaunt the fact that you're a tourist by donning a money belt or dangling a camera around your neck. Don't put valuable objects on display and keep an eye on your belongings when using public transport.
On the subject of drugs, you know the deal - leave them well alone.
In the unlikely event that you're attacked, don't resist, hand over whatever it is they want and try to remain calm. It's wise to never keep all your money in one place. Hide cash in different places and only keep enough to appease a thief within hand's reach.
As far as dangerous zones in Armenia go, just avoid them at all costs. If you don't have a choice, check out the current situation with the Armenian Ministry of Foreign Affairs.