A well-known technique in filmmaking and animation when designing a creature is to vary the size of the creature's eyes. If you want your creature to appear cute, give it eyes that are excessively large for its body. If you want your creature to appear huge, give it relatively tiny eyes. If you want it to be both huge and cute, pay close attention.

This trope could be a result of one of the many shortcuts the human brain makes when calculating its surroundings: Because most small, harmless animals (possibly including human babies) have large eyes compared to their heads, we are programmed to find that trait cute, while most things that are liable to eat us have small eyes, so we are programmed to run when we see them.

Alternately, it could just be that big eyes are much more expressive than little eyes, which leads to Good Eyes, Evil Eyes when used for people in animation. Puppy Dog Eyes are a subtrope.

Examples of Big Eyes, Little Eyes include:

Examples of cute critters with big eyes

Anime and Manga

Kirara from Inuyasha, both in her small and large form.

Film

Toothless from How to Train Your Dragon manages to pull off both. His pupils contract and dilate based on his mood. It makes him ridiculously adorable.

Live Action TV

The Muppets in Sesame Street generally have big googly eyes, to appeal to children.

Literature

Lewis Carrol, known for inventing many ideas used in cartoons and modern fiction, may have been the Trope maker in his 1800s book Alice in Wonderland in which Alice shrinks and literally encounters a puppy with large eyes.

Real Life

Truth in Television: kittens, puppies, babies.
- Pandas are quite large, and do in fact have small eyes. However, one of the reasons they are considered cute is probably that they have black circles around their eyes, making them look like they have bigger eyes than they do.
Subversion: The largest eyes in the world belong to the giant squid, which is probably among the more frightening animals in the world.
- That owes largely to the excessively alien appearance of the giant squid. The form of the animal and the shape and position of the eye give it a horrific zing, like if you found someone's eye sitting on a plate in front of you.
  - Also from the fact that the sharp eyes of Cephalopods evolved in a complete different way to tetrapod's, just like the wings of birds and insects.

Web Comics

The Jinxlets from Starslip Crisis

Video Games

Pokémon: Often when Pokemon evolve into their next forms, their eyes usually become smaller or less pronounced as an indication of maturity. Examples: Bulbasaur to Ivysaur to Venasaur, Vulpix to Ninetales, Sunkern to Sunflora, etc. However, there are exceptions where Pokemon have larger eyes than their pre-evolved forms (Torchic and Blaziken come to mind). And Zubat has no eyes at all.

Examples of huge critters with little eyes

Film

The Sando Aqua Monster from Star Wars Episode I: The Phantom Menace.
Used with a twist in the first Jurassic Park, where the dinosaurs have little eyes, like they did in nature. Then the T. rex gets right up next to the jeep and peers in, and that eye that looked so small from a distance turns out to the size of the kids' heads, which re-emphasizes the sense of scale.
The original Gamera. Subsequent movies in the series reworked the rubber suit to give him bigger eyes, and the sense of scale is lost.

Real Life

Truth in Television again: elephants, whales, big dinosaurs
Subversion: Moles, naked mole rats, or any other subterranean animal.

Western Animation

Big Dog from Two Stupid Dogs has beady little eyes under his Blinding Bangs.