Sideways Smile

And no, despite what you may think, it's not: :-)

This is another artistic convention seen in anime and manga, and most commonly in comedy material.

Even when a character is facing away from the viewer and only a narrow part of the side of the face is visible, facial expressions are still apparent, especially a sneaky smile that crawls up the cheek and almost reaches the ear. Real flesh-and-blood humans are anatomically incapable of this, but drawn characters suffer no such limitations.

Can be used to hide a Psychotic Smirk.

Examples of Sideways Smile include:

Anime and Manga

Early in Inuyasha, Sesshomaru smiles like this... and the smile keeps going, becoming a fanged muzzle as Sesshomaru takes on his true dog-demon form.
Haruko in FLCL does this a lot.
- Kamon as well.
The OVA version of Hellsing does this a lot with the "face splitting smiles" of the original manga.
Many characters in Crayon Shin-chan do this, though Shin and Hima do it the most.
Nausicaa of the Valley of the Wind: Kurotowa seems to have one perpetually plastered on his face. Ironically, Chris Sarandon seems to share that trait.
Lust does this early on in the Fullmetal Alchemist manga. Combined with Psychotic Smirk.
Plenty of characters in Soul Eater get this, particularly Soul himself when the little demon gets in on the action.
It may not come as much of a surprise that both Kamina and Simon get in on this in the course of Tengen Toppa Gurren Lagann, most notably in the first time each of them gains their respective mecha.

Live Action TV

The semi-animated opening credits to the 1960s TV series Batman.

Music

The cover of the Rolling Stones spinoff album Jamming With Edward (yes, that's where Cowboy Bebop got one of its episode titles from) features a cartoon strip by Nicky Hopkins, in which a sideways smile literally splits a character's face in two causing the top of his head to fall off.

Western Animation

Toph in Avatar: The Last Airbender uses this whenever she's about to do something impressive.

Video Games

As a result of this, Sonic the Hedgehog's mouth is on one side of his face.