Scars can add a lot to a character, but it's important to do it right.
Here's my thoughts on them, and while you might not agree on everything, I suggest you at least consider the cause of the scars before adding any to your character.
I've split it up into sections to consider when deciding if your character should have scars and where.
Career and professionEdit
Having scars just because they look cool is not very interesting, and depending on what they do for a living, they might not have any at all. A seamstress isn’t likely to have knife scars for example. On the other hand, a guardsman from Duskwood is unlikely to have escaped without at least a couple of scratches here and there.
Scars can also depend on what your character's professions are. If they are an Engineer it's likely they'll have some burn marks or cuts, and if they are an Alchemist they might have some small acid burns, or cuts from sharp herbs or broken glass. These two professions can both cause burns and cuts, but the cause of them are very different, so the shape and size will be too.
Hunters and animal trainers will almost certainly have bites, cuts and scratches. Maybe even scars from accidentally setting off their own traps. -It's important to consider how naturally skilled they are as well.
Race and SizeEdit
Take into account how tall and wide your character is. Gnomes and Dwarves are most likely to have battle scars on their faces and high on their body rather than lower down, as nobody would be swinging a blade around at ankle height. Whereas Draenei would likely have more around the middle and on the legs. Worgen are likely to have claw marks from the transformation and maybe hunting or fighting other Worgen. They're often obvious, but might also be something your character is self conscious about and want to hide.
Think about what a character feels about the scars they have as well as just how they got them.