Most often facial hair appears somewhere between stubble and a full beard. Often times facial hair is left as is, undetailed; however, in many famous cases they are detailed into that of a goatee (like that of Gordon Freeman in the Half-Life series, or Solid Snake in the Metal Gear Solid series), a spectacular mustache (like that of Captain Price in the first Modern Warfare), or a plain mustache (like that of Old Snake in Metal Gear Solid 4).
Sideburns, muttonchops and the like are the least noticeable of facial hair except in a few cases such as that of Eddie Riggs in Brütal Legend.
There are many styles of beard type facial hair some of which can be chosen in various character creators. As with beards many mustaches are also available in character creators in various games.
The first video game character with facial hair was Mario, with his mustache. He wasn't originally intended to have a mustache, but had it due to technical hardware limitations when he made his debut in Donkey Kong (1980). Because a realistic mouth was hard to draw at the time, Mario had a mustache, which eventually became a signature character trait.