I'm doing this in Ultima Ratio Regum. The way you face affects:
a) fields of view. You can only see in a 160o/170o area in front of you, you cannot see behind you. The same goes for NPCs - you can see which way NPCs are facing, and that will obviously affect if they can see you, or only hear you.
b) attacking. If you attack an NPC from behind, you might able to attack their back (so spine, hamstrings, etc), whereas attacking an NPC from the front will give you access to different parts. The same applies to NPCs attacking you, of course.
c) It also takes a turn to change what direction you are facing. It is a quicker activity than moving in terms of turns-elapsed, but changing the direction you have takes time. Equally, if you are sprinting, for instance, you cannot suddenly change direction. If you are sprinting to the west, you can change direction to NW, SW, N or W, but trying to change to any of the "backwards" directions will force you to slow back down to walking.
d) what you can do/throw/look at: you can only examine objects in your sight range, you can throw in any direction but obviously you won't know what you're doing if you throw "backwards", and similarly you can jump in any direction, but there's a risk in jumping in unknown directions.
e) I intend, later, to implement the ability to sidestep, and also the ability to move backwards whilst still keeping your vision int he same direction. There might be more factors too, but I can't bring them to mind.