Honduras has a very high crime and violence rate, though the vast majority of travelers experience no problems. Pickpocketing and petty theft are the most common, and assault is possible. Take ordinary precautions - don't wear flashy jewelry, walk around with your camera out or pull out wads of cash. Tegucigalpa and San Pedro Sula are the worst places for street crime; the downtown areas of both are fine during the day, but less so after dark. Consider taking a cab when it gets late. If you are mugged, do not resist.
In general, small towns are safer than the big cities. Watch yourself on the north coast, especially on the beach: avoid leaving items unattended and stay away at night. It seems to be a favorite tactic of thieves to wait in the trees along a deserted stretch of beach, especially after dark, and wait for someone to come by.