In the natural world, living creatures have a myriad of ways of bringing more young into the world. Some produce thousands of eggs and young that grow quickly but only a few make it to adulthood. Others invest huge amounts of time and resources to develop and take care of only a few at a time.
In fiction, it's often simplified into laying eggs, even if the biology of the creature in question should indicate otherwise. This is very useful in bypassing the complications of an Interspecies Romance and the Squick of a live birth, which is also why it's a common implementation of G-Rated Sex.
Popular Mons trope, as pretty much every Mons series uses it. Especially the ones that originate in Video Games, where it also serves to simplify the breeding mechanics — see Hot Skitty-on-Wailord Action.
Anime and Manga
Digimon, though Digimon are asexual so the eggs actually spawn from the remains of dead Digimon. Since the Digimon that "spawn" from this act are actually the same individual Digimon that died, it works as a Disney Death. Though several cases could result in real death for good, such as fights taking place in the real world, or if someone manages to invent a device to get rid of that feature. It depends on the season.
Fairy Tail: Happy hatched from an egg. Supposedly, so did his Romantic Interest Carla. Their species, for reference, resemble bipedal cats. Their eggs are also larger than full grown members of the species, in case the fact that they technically aren't cats made eggs seem plausible.
Tenchi Muyo! had Ryo-Ohki, a cat/rabbit creature who can turn into a spaceship and a humanish girl, hatch from an egg. In addition, Ryoko joked that the egg was hers and that Tenchi was the father, but it later turns out that, in a really convoluted way, the egg came from Washu.
Although Domo appears to be mammalian in nature, his first appearance was being hatched from an egg.
Namekians are asexual aliens that reproduce by spitting eggs infused with some of their life force.
Skrulls lay eggs. Johnny Storm, who was briefly married to a Skrull named Lyja (long story), was greatly disconcerted when she... well, laid an egg. It turns out it wasn't his, though. Which was... good news and bad news at the same time, kinda.
This was subverted in an Archie Comics story, where Jughead had to take care of what he thought was a kangaroo egg in Professor Flutesnoot's laboratory, until Mr. Weatherbee showed up and informed Jughead that kangaroos don't lay eggs. When the egg did hatch in the end, it turned out to actually be an ostrich egg.
The Easter Bunny, according to some. They're not all chocolate, you know. Mythologically, the bunny originated as a egg-laying animal; being able to lay eggs once a year was a form of consolation (the day was only later retconned to Easter). Of course, in the original myths the bunny wasn't Peter Cottontail.
In Greek mythology, Leda, the human queen of Sparta, has sex with Zeus in the form of a swan, and later with her human husband Tyndareus. She lays two eggs, one containing Castor (usually the son of Tyndareus) and Polydeuces (son of Zeus), the other containing Helen (usually daughter of Zeus), later of Troy, and Clytemnestra (daughter of Tyndareus). The parentage and pairing of these children is not consistent, but the story always involves two completely normal human children hatching from eggs.
In Korean Mythology, many founding heroes of ancient kingdoms (three kingdoms) were born from an egg. Here are examples:
Go-Jumong (King Dongmyeong), founder of Goguryeo Kingdom, was born as a large egg that his mother (Lady Yuwha) laid. His stepfather (King Geumwha) took this as bad omen and tried to get rid of it, but all attempts failed (when it was thrown into wilderness, fierce animals and birds kept it warm; and even the strongest warrior couldn't break its shell open). Finally Jumong was born, and he soon grew up to be a master archer and charismatic hero (which is not surprising, given that his father is the ''Sun god Haemosu'').
Theres also Pakhyeokkeose, Seoktalhae and Kimalji, three founders of Silla Kingdom. Plus there's King Kim Suro, founder of Gaya (a minor kingdom that was later absorbed into Silla).
Sun Wukong technically hatched from a rock, but it's often referred to as the Great Stone Egg. More literal to the trope, Pan-Ku, the first living being, hatched from an egg that became the sky and the ground.
Happens as a (disturbing) twist at the end of the Goosebumps book ''Egg Monsters From Mars".
Subverted in Tamora Pierce's short story Nawat. The titular character's wife does not lay eggs, despite her fears. Instead, one of the babies takes after her crow-to-human shapeshifter father by eventually growing some feathers.
At least two of the races (namely, the chiropteran Aeries and the near-humanWalkers) in Laurie J. Marks's Children of Triad trilogy seem to be monotremes.
Played With in Dr. Seuss' Horton Hatches the Egg: Everybody flocks to see the (male) elephant sitting on an egg, but it was actually laid by a bird who asked Horton to egg-sit (though it's unclear if the mother planned to come back). At the end, this trope turns out to be a case of Lamarck Was Right, as the egg hatches into a winged elephant.
Bomberman: Blowing up a soft block in later games will sometimes yield a giant egg. Touch this egg, and an adorablekangaroo hatches. (Averted in Saturn Bomberman, because they're dinosaur eggs instead.)
Billy Hatcher and the Giant Egg has them all over the place, generally used as weapons and movement aids. Things that can hatch from these eggs include tigers, butterflies, winged fire-breathing hippos, and Sonic the Hedgehog himself, among who knows what else. It's even lampshaded when an NPC chick wonders who or what laid all of these eggs to begin with.
Spore: Every creature hatches from an egg, be it lizard-bug, or snake-monkey, or what have you.
Final Fantasy Tactics: Every monster that joins you reproduces asexually by laying eggs. Makes sense for the Chocobos, gets strange for the cats, skeletons, trees, and pigs.
Creatures: The Norns and Ettins look mammalian (and one popular third-party breed for the second game was able to nurse their young,) but all three creature types lay eggs (of course, they were all genetically engineered by an entire species of extremely absent-minded scientists, so they don't necessarily have to make that much natural sense). The scientists were also so squeamish (canonically!) as to have to invent kisspopping, so whatever process results in the eggs, they likely found it more emotionally palatable than seeing a miniature version of the Norns (et. al.) being shoved out of an orifice of another.
There is one exception. A diary entry in the Cinnabar laboratory states that "Mew gave birth." Mew is also among a subset of Pokémon that are functionally genderless and never lay eggs. On the other hand, the birth may or may not have happened, as every piece of information on Mewtwo's origins are contradicted somewhere else. It could have been just a metaphor, since it is said that Mew's genes were used in the creation of Mewtwo.
The Facebook game Fish World lets you gain new creatures for your virtual aquarium by buying "Fish Eggs". The, err, "Fish" include everything from crabs to turtles to squid to, yes, Whale Eggs.
Collecting chicken-style eggs that will hatch out into all sorts of creatures — birds, mammals, frogs, fish, bugs, trees, VAMPIRES — is the whole point of the Facebook game Hatchlings.
The plot of The Legend of Zelda: Link's Awakening is to break the ostentatious egg of the Wind Fish, which is essentially a gigantic, telepathic whale with disproportionate wings! (Also to fight evil Kirby clones, but that's irrelevant at the moment.)
There is an entire genre of games for tablets and mobile devices where the player builds some type of haven, fills it with decorations and/or enclosures, then breeds and/or feeds various monsters and critters. These frequently show the monsters hatching from eggs, even when the monsters look mammalian, such as in My Singing Monsters.
In the Guilty Gear series, newborn Gears apparently hatch from eggs. This explains how Justice's daughter Dizzy was born years after her mother's demise.
Putty has a Mutant Chinese Chicken which lays sumo wrestler eggs.
According to his mother, Little One of Tales From My D&D Campaign hatched from an egg (he's half-dragon). Made even weirder by the fact that she also claims to have spent the entire pregnancy in her human form, which is why Little One manifests so few visible marks of draconic heritage.
Played with on American Dragon Jake Long. Jake spends an entire episode protecting a griffin egg, finally returning it to its mother. It then hatches...and the mother eats the baby. While Jake is horrified, Fu Dog calmly explains that since griffins are half-bird and half-lion, the mother just needs to carry the baby the mammalian way for a bit. Oddly, we have to presume the dragons actually don't come from eggs, since Jake's dad still doesn't know what's going on. Then again, these dragons are human most of the time anyway.
Inverted in Franklin and the Green Knight where they show Mrs. Turtle being pregnant rather than showing Harriet (Franklin's baby sister) hatching out of an egg.
In the My Little Pony: Friendship Is Magic episode "Luna Eclipsed", Pinkie Pie is dressed up as a chicken for Nightmare Night. At one point she get so spooked she lays an egg. A dragon egg. Somehow.
Inverted with Kif who is an alien who is basically humanoid, but has Bizarre Alien Biology that points to him being some sort of amphibian. When he gets pregnant, however, he winds up giving birth to a collection of tadpoles. It's an interspecies example, too, as the biological mother is Leela.
Leela mentions that she occasionally lays an egg, more than likely, due to her mutant DNA.
The Duck-Billed Platypus and Echidnas are the only living mammals to lay eggs. As an ancestral trait, egg-laying was probably much more common among mammals in the past, but by stroke of luck only a few lineages have survived to present day.
Tsetse flies. They even raise their larva on a bug analogue of milk while they are developing.
Beluga caviar sounds like this trope, but sadly, it's actually eggs from a fish called the Beluga Sturgeon.
Technically every species that doesn't reproduce asexually do come from fertilized eggs. It's just in the case of most mammals that the infant is incubated in the mother's womb instead of in a shell. (Yes, plants come from eggs too! We just call them seeds.)
Here's some weirdness for ya. A good portion of mammalian DNA is non-sequencing, or "junk" DNA. That doesn't mean it doesn't do anything, though. For example, some of that is very important in allowing a fertilized egg to attach itself to the uterus. Some of that comes from Endogenous Retroviruses which basically means that an ancestor was infected with a virus that incorporated itself into their genetic code and passed it on to all future generations. Putting all that together has lead scientists to theorize that it was a viral infection that allowed modern fetuses to bypass the mother's immune system and necessitate live births as opposed to eggs, splitting reptiles and mammals.
While human fetuses don't have eggshells surrounding them, they do have an amniotic sac, which corresponds to the clear membrane just inside an egg's shell. Usually this splits apart and peels cleanly away from the infant before the latter emerges from the birth canal, but occasionally the sac (called a "caul") will still be wrapped around the newborn after parturition.