As characters can turn freely as they move they can also 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 move, 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 or behind him to worry about looking round for fresh targets.