Harlequin Shadowseers in Warhammer 40,000 wear face-concealing, featureless masks in combat (and outside of it?), ensuring that the last thing the enemy sees will be the reflection of their own face (though the implication is that it goes beyond a reflection, and the enemy literally feels as though they are fighting themselves). On that note, all other Harlequins use masks as well, but theirs have actual theatrical expressions.
In Exalted, the god Nara-O is always covered in thick dark bandages that completely obscure his features. As the god of Secrets Known To One Person, it is suspected that if any being besides himself was to know his appearance, he would cease to exist.
In the Pandemic expansion On The Brink, the Bioterrorist is depicted clad in a chemsuit, with no indication of hir sex or ethnicity.
ApocalypseWorld features the player character class 'The Faceless,' a mask-wearing thug. If their mask is removed, it's always treated as The Reveal, stunning everyone nearby and freaking the Faceless out.
Magic The Gathering: Arcanis the Omnipotent wears a hood that conceals his face, and Eldrazi of the Ulamog lineage have heads covered entirely in bony plates. Honourable mention to Ashiok, Nightmare Weaver, a planeswalker whose entire head is transforming into black mist, who isn't The Faceless yet, but is well on zir way.