Creepy Shadowed Undereyes

One way to make a character look creepy is to have deep, dark circles surrounding their eyes in the form of shadows or natural pigmentation, giving them a creepy skull-like, or sinister appearance. Often goes hand in hand with Eerie Pale Skinned Brunette and Evil Old Folks and combined with Evil Eyebrows.

A character that Looks Like Cesare tend to have these eyes, also The Insomniac and other deranged characters, as eye pigmentation can happen from physical exhaustion and lack of sleep, though if it's a one off gag, then they are Exhausted Eye Bags. Some characters may artificially try to replicate this effect with make-up, resulting in Excessive Evil Eyeshadow, or Guyliner, but it just doesn't have the same effect and is not the trope.

When the whole eyes are in shadow to the point that you can't make them out at all they are Hidden Eyes. this effect may be induced or go hand in hand with a Kubrick Stare.

Anime and Manga

 * L from Death Note, an Eerie Pale Skinned Brunette, has circles around his eyes so dark, he has the fan nickname "Panda".
 * Light in the manga is shown to have dark circles around his eyes as well after he became Kira.
 * Colin from Two Keys who is an Eerie Pale Skinned Brunette with huge dark circles around his eyes, which sometimes double as Hidden Eyes, reflecting both his dark past and mysteriousness.
 * Kuroki from Its Not My Fault I'm Not Popular has these. While she's not exactly a bad person, it does reduce her physical appeal and reduces her self-esteem.
 * Miranda from D Gray Man, though heroic, has these to reflect her gloominess and lack of sleep. They also add to her Eerie Pale Skinned Brunette appearance.
 * Almost every character in Houkago Play has this - partly because many of them are hardcore gamers, and partly because of the art style.
 * Itachi Uchiha from Naruto manages this in his more serious ass-kicking moments.
 * In the original Japanese, Gaara's darkly circled eyes are expressly stated to be Tankui-like marks he was born with, signifying the animal his bonded demon looks like, much the way Naruto has whisker-marks. In the English dub, they were explained to be caused by his insomnia, which not only makes sense (rather than just assuming the audience wouldn't know what a Tanuki was or just calling it a "raccoon demon") but significantly ups the creep-factor.
 * Trafalgar Law, the  'Surgeon of Death'  from One Piece.

Film

 * Frollo from Disney's The Hunchback of Notre Dame actually has purple eye shadows.
 * Betelgeuse from, well, Beetlejuice has dark rings around his eyes. This is actually due to the fact that Tim Burton originally conceived the character as having no eyes at all but changed his mind after noticing how expressive Michael Keaton's eyes were.
 * Gaston gets these in the last third of Beauty and The Beast, to show that he's a Not So Harmless Villain now.
 * Disney villains in general.
 * Mike, by his second trip to the loony bin, in Truth or Dare?: A Critical Madness.
 * Played for laughs in Fiddler On the Roof during Tevye's "dream" sequence; all the dead departed have them.

Literature

 * In Street Magic, Jebbun Stoneslicer has eyes like these.

Live Action TV

 * The Addams Family, this is one of Wednesday's most pronounced features, as she's an Eerie Pale Skinned Brunette.

Video Games

 * The Medic in Team Fortress 2 has these. They're fairly subtle, but compared to the other characters it's a reasonably noticeable feature. It's probably to make his eyes stand out behind his glasses, show that he's no spring chicken, and suggest that he's the kind of person who likely stays up late doing horrible medical experiments. And maybe the stress of his thankless job is getting to him.
 * The Thwomps from the Super Mario Bros series games.

Webcomic

 * Gunnerkrigg Court has Jack while he was . Averted by Winsbury, who's a Jerkass initially, but otherwise completely normal. Zimmy (who's eyes are completely covered in black gunk) has these even when her eyes are washed out.
 * Azuu of Elijah and Azuu has visible bags under his eyes constantly, but he doesn't have it nearly as bad as his son, who has very obvious Creepy Shadowed Undereyes (and both also have a case of Red Eyes Take Warning to boot)
 * In Homestuck, many of the Trolls have this.

Western Animation

 * Several Danny Phantom villains have dark circles under their eyes for the look of evil, starting with Vlad.

Other

 * Svengoolie. The actor uses makeup, but the it's the characters natural look.

Real Life

 * In Real Life the skin around the eyes is much thinner, so some people do have darker areas around their eyes (it's also the reason bruises around the eye are so prominent).