Because characters can turn freely as they move they can be turned to face any direction once they have moved in order to see a target the character intends to shoot at, for example.
The exception to this rule is if the character makes a compulsory move, such as a charge, flee or pursuit, in which case the model must finish its move facing the direction of travel. Obviously, in this situation the character is far too preoccupied with what is in front of him to worry about looking round for fresh targets.