There's considerable crime in Belize City, but it rarely involves visitors. When it does, Belize has a particularly rapid justice system for such crimes, meaning that the offender often gets a trial within hours and, if convicted, can be sent to prison ("the Hattieville Ramada") the same day. Tourist police patrol Fort George and other areas of Belize City where visitors convene. Police are particularly in evidence when cruise ships are in port. If you avoid walking around at night (except in well-lighted parts of the Fort George area), you should have no problems in Belize City. Outside of Belize City, and possibly the rougher parts of Dangriga and Orange Walk Town, you'll find Belize to be safe and friendly.
Most Belizeans are extremely honest and trustworthy. It's not uncommon for a vendor to chase you down if you accidentally leave without your change. That said, most organized scams arise with tours and packages, in which you're sold a ticket that turns out to be bogus. Arrange all travel through a legitimate agency, and always get a receipt. If a problem does arise, the Belize Tourist Board may be able to help mediate the conflict.
Many women travel alone or in small groups in Belize without any problems. Machismo is not as much a factor in the former British Honduras as it is in Latin countries in the region.
