Pie-Eyed

During the 1920s and going into the 1930s, animated characters tended to have eyes or pupils which were black and circular, but shaped like a pie that's had one slice removed from it. This was widespread until around the time color became the standard for most cartoons in the early 1940s, by which time the Inkblot Cartoon Style had fallen out of favor, and Western Animation as a whole had undergone significant Art Evolution.

When it shows up in modern media, it's usually as an homage or throwback. Parodies of the Inkblot Cartoon Style will almost always employ this along with Rubber Hose Limbs and the like.

See also Black Bead Eyes. Not to be confused with a slang term for being drunk.

Examples from The Golden Age of Animation:

Betty Boop, and most of her supporting characters.
Dinky Doodle
Porky Pig, in the 1930s.
Bosko the Talk Ink Kid, Depending on the Artist.
Mickey Mouse occasionally sported these eyes (as seen in the above image) in his early days, when he didn't just have Black Bead Eyes. It sometimes went between the two within the same exact short.
The characters in the Merrie Melodies short I Love to Singa, a rare color example.
Felix the Cat in some shorts.
Foxy from Merrie Melodies.
The Coachman's Nightmare Face from Pinocchio.

Modern Examples and Homages

Anime and Manga

In Bobobo-Bo Bo-bobo, Don Patch sometimes has these eyes.

Film

The animated segment in Johnny Dangerously uses them, as it's done in a 1930s art style.

Music

The song "The Ghost of Stephen Foster" by the Squirrel Nut Zippers had an Animated Music Video that paid homage to the Max and Dave Fleischer cartoons of the 1930's. Every character in the video is pie-eyed.

Video Games

Appropriately enough, when Pac-Man is pictured in his mascot form (as having arms and legs) he usually has these eyes. It shows up on the arcade cabinet art, and in later games such as Pac-Man 2: The New Adventures and Pac-Man World.
MOTHER 1 clay models had these kind of eyes on Ninten and Ana. Loid and Teddy's aren't apparent because they wear Opaque Nerd Glasses and Cool Shades respectively. This is another rare modern usage that is not a throwback. However, the characters in the two sequels feature Black Bead Eyes instead.

Web Comics

Gastrophobia has a Western storyline drawn in this style.

Western Animation

It was used in the Two Stupid Dogs short "Hobo Hounds", which was made to look like an old silent cartoon.
My Life as a Teenage Robot, which uses a Retraux style.
Toot Braunstein from Drawn Together, who is a parody of Betty Boop.
SpongeBob SquarePants: In the 10th Anniversary episode, Patchy shows a SpongeBob short in a 1920s style, where everything has this eye style.
In the Powerpuff Girls episode "Silent Treatment", the girls gain these when they get trapped inside a silent cartoon.
Mostly everyone in The Super Mario Bros Super Show cartoon has this feature, a rare modern usage not meant as a throwback.
Mr. Hanky, from South Park.
The Futurama episode "Reincarnation," which parodies several animation styles, gave these to the cast in the 1930s-style segment.
The characters in Happy Tree Friends.

Real Life

Cat clocks with moving eyes often are pie-eyed - sometimes referencing Felix the Cat, sometimes referencing other cat clocks.