The one on the box? But what about the actual DoomGuy in the Doom 1 and 2 (not the one on the title screen)? You see his face the whole time you're playing! Of course, that camera could be inside his helmet, I suppose.. when you play multiplayer (in any of the Dooms), all the players are wearing helmets, but I always figured that was just so it wouldn't seem like everyone had the same character.
In Doom 3, it certainly would make sense for the main character to wear a helmet (I mean, there are several sections where you go outside and your 'oxygen tank' starts draining.. although at the speed it drains it almost seems like your guy is holding his breath), but he is never actually shown with one.