The crime rate in Belize is one of the most heated topics. You'll find every different opinion imaginable. Some people feel perfectly comfortable, others are extremely cautious. But what it really comes down to is like what DrSteve and bonbon said: Some areas are better than others, and you really have to try Belize out and decide for yourself whether you feel comfortable enough to bring children down.
Some people regret moving to Belize, others regret not doing it sooner.