In the grand scheme of things, Honduras it still very young when it comes to tourisim. As such, the country has done little to enforce safety in most of the major tourist areas. This point is not meant to scare you away from visiting Honduras, but more to make sure you are aware of the dangers so that you can protect your self from them.
A little street smarts and common sense can go a long way to protect you and your belongings. The obvious rule of not going out a night is one to practice here. If you insist on going out at night, under no circumstances should you go out alone or with any sort of bag or purse. Both of these are just asking for trouble.
The above is especially true in the cities of Tegucigalpa and San Pedro Sula. San Pedro Sula has the highest murder rate of any city in the country. Though most of it is between rival gangs over territories. if you must go out at night, do so with a dispatched taxi only.
Avoid public transportation if you can. Riding buses makes you a prime target for pickpockets and petty thieves. You will also want to avoid un-dispatched taxis ( ones without radios) and taxis with dark tinted windows. taxis with dark windows can be an open invitation to get robbed inside the taxi.