Only Six Helmets

Games that try to avoid Only Six Faces often offer a wide range of customization options for the player. This can be achieved by letting the player choose from a palette of pre-made faces, or, like many newer games, letting them change single elements of the face with sliders, thereby making it theoretically possible to create thousands of different faces.

Then the player decides to play a warrior, and after ten minutes of playing he finds his first helmet. Which covers the character's face entirely. Wait, why did we spend half an hour at character creation again?

Usually, you can take it off again if you don't like this, but, depending on the difficulty of the game and the usefulness of the helmet, this may be a bad idea.

Averting this is one of the Acceptable Breaks From Reality (because not wearing a helm in real combat is pretty dumb); see Helmets Are Hardly Heroic.

Note that this does not apply if there is no Character Customization. This is solely about wasted customization (because we can't see it). Also applies to hairstyle or anything else that's immediately covered by armor.

Many games allow you to toggle your helmet showing up, so you can still gain the benefit, without obscuring your character.

MMORPGs

 * Guild Wars suffered from this, but it was since changed so that displaying the headgear could be turned off, without losing its benefits.
 * World of Warcraft, although the player can choose not to display it or transmogrify it into a different helmet of the same armor class.
 * Maple Story has several face-obscuring helmets, but, graciously, they're limited to the lower levels. And there are still more helmets than there are faces.
 * Dungeons and Dragons Online has a fairly wide selection of helmets, and most of them don't even cover your face. Sadly, all of them cover your hair, which comes in a variety of styles and colors, some of which are only available at the in-game store. Fortunately, there is a Slash Command that turns a character's helmet invisible.
 * Global Agenda, though there's something like 20 helmets per class per gender, and then colors you can layer on, but you undoubtedly spent a long time making your first character's face, and there are vastly more face-customizing options than helmets. Once you get your first helmet, you often never see your face again.
 * Averted in DC Universe Online, as the appearance of a character and the effects of their costume are not necessarily the same.

Role Playing Games

 * Morrowind: All helmets erase the hair and most helmets cover the face as well.
 * Especially glaring because your armor bonus depends on wearing armor over all parts of your body, so skipping the helmet because you want to show show your character's face means you're going to take a hit on your entire defense.
 * Oblivion: Pretty much the same, although there are more helmets that leave at least parts of the head visible.
 * Power Armor helmets and some additional headgear (ski masks, welding masks, raider wastehound helmets) in Fallout 3 cover the entire face. Some outfits like hazmat suits or the stealth armor cover the entire body including the head.
 * Not even an hour into Dragon Age will pass before you procure your first helmet, wasting your hard-spent moments creating the perfect nose for your human noble.
 * A popular mod for the PC version allows helmets to appear unequipped only to be automatically equipped for combat and when you open the menu. It's not without its bugs, however.
 * Dragon Age II included a feature that allowed the player to hide his/her helmet while keeping it's stats.
 * In the little-known Siege of Avalon Anthology, you don't get much to customize--just hair color, hairstyle, and whether you have a beard, but every one of the three dozen or so hats, hoods, and helmets covers at least the hair, and usually the face (and beard) as well. However, the non-magical ones are practically useless anyway (giving only 1-2% damage reduction), so going without is perfectly plausible.
 * Hellgate London has Only Six Faces, but out of the nine different helmets (18 if counting gender-specific models for each) all of the Templar and Hunter helms conceal some nicely modeled facial features. Going bareheaded isn't recommended, and the stat bonuses are too good to pass up.
 * In Mass Effect 2, you can procure several different types of headgear for Shepard to wear, all of which provide some sort of stat bonus, and almost all of which cover most (if not all) of the face you spent ages getting just right. Luckily, the stat bonuses, while useful, aren't that big, and going helmet-less isn't a huge risk. However, during certain missions (unless Shepard is already wearing a full armor set), the game will force Shepard to wear the N7 Breather Helmet, which covers everything except his/her eyes.
 * Speaking of the full armor sets: the number one complaint about them is that they all have non-removable helmets which cover Shepard's face entirely. Since most of the game's cutscenes occur while (s)he's in his/her armor, this can cause some...strange situations, such as Shepard being able to drink liquor through his/her faceplate, or people recognizing Shepard by sight despite the fact that (s)he's dressed head-to-toe as a Collector.
 * Wearing a helmet with a face mask also causes Shepard's voice to sound like it's coming from a speaker which can get annoying at times.
 * Monster Hunter has a wide variety of customization options for faces, but helmets cover up all of that. You can slightly change the color of the helmets, but it is typically a small change.
 * Temple of Elemental Evil; luckily, helms have no in-game effect, except for the magic ones (and most of them are headbands).

Sandbox

 * Terraria allows you to choose a hairstyle and hair color (sometimes with facial hair) for your character. It even lets you use the entire 24-bit color spectrum to do so. But, once you get that first helmet, kiss that hair goodbye (barring certain social helmets worn on top of it), including the facial hair, as there's only one sprite for each equipped helmet, and that sprite has no hair.
 * There is a wig you can wear, which you put over your helmet so you look hatless. It's really hard to get hold of it, though.