Male penguins of many species gift their mates with rocks.
Female penguins don't rely on pebble presentation as a key aspect of mate selection;, and penguins don't appear to care as much about the characteristics of a pebble so much as its ability to add to their nest.
A popular "Did you know?"-style assertion holds that penguin mating rituals closely mimic human courtship, in that the male's finding just the right symbolic gift to present to his female of choice is of the utmost importance:
When a male penguin falls in love with a female penguin, he searches the entire beach to find the perfect pebble to present her. When he finally finds it, he waddles over to her and places the pebble right in front of her. It is like a proposal.
According to the story (which can be found on multiple amusing, if not very credible, fact-based social media accounts as well in the 2007 film Good Luck, Chuck), when male penguins fall in love, they search an entire beach for the "perfect pebble." (No specific criteria determine what makes a pebble "perfect" by penguin standards, such as size or color.) After evaluating every pebble on the beach, the courting male penguin then lays the prize at the feet of his selected mate, a rite that is typically framed as an avian version of the human custom of engagement rings.
Marine life theme park franchise SeaWorld maintains a virtual exhibit on penguins, part of which chronicles their mating habits. While pebbles do get a mention in that exhibit, it does not describe the stones' supposed perfection as having much to do with the process of wooing a mate:
[Adélie penguins] build nests of small stones that they use to line depressions in the ground. Some chinstrap and gentoos also construct nests out of stones. The stones help keep the eggs above the surface when the rookery floods from melting snow. Adélie, gentoo, and chinstrap penguins are known to take stones from other nests. A penguin returning to the nest sometimes brings its mate a stone as a courtship gesture ... One medium-sized gentoo nest was composed of 1,700 pebbles and 70 molted tail feathers.
According to SeaWorld, stones and pebbles are about as romantic as stucco or siding to various species of penguin, although they do seem to serve occasionally as practical gifts.
Antarctic researcher Guillaume Dargaud (who says that he "lived with penguins for more than a year" but is "no substitute for a real ornithologist") addressed the rumor on his comprehensive page devoted to Adélie and Emperor penguins. Dargaud dismissed the rumor as a myth attached to the nest-building habits of Adélie penguins, opining that the collection of pebbles runs coincident with the mating process, but that any pebble would suffice for the purposes of mate evaluation:
Q: I heard that when Adelie penguins are choosing a mate the male searches for the perfect pebble and presents it to the one he wants as his mate.
A: It's a myth based on the fact that Adelie penguins build nests out of pebbles. And they build the nest while they do the courting, so it's actually partly true. I guess a penguin who doesn't bring any pebble wouldn't stand a chance, but any pebble will do and both mates bring them in!
We also contacted penguin expert Dyan DeNapoli for further clarification on the penguin pebble presentation rumor. DeNapoli explained that stones can play a role in the mating rites of penguins, but typically penguins aren't partial about what types of pebbles end up in their collections:
Some, but not all, penguin species collect rocks for their nests. Of those that do, the purpose of the rock collecting is to build an elevated nest so the eggs and/or chicks won’t get wet or drown when it rains or when the snows melt. Some penguin species collect twigs and other plant materials, and the two largest penguin species – the King and the Emperor – don’t build any nest at all. They carry and incubate their single egg on top of their feet.
As for the searching the beach for the perfect rock, some penguins do seem to be selective in choosing rocks, and will trot off some distance in search of the right one. Other penguins, however, are quite content stealing rocks at random from neighboring nests. They’re not usually very selective – it’s done very quickly before the neighbor returns to their nest.
In most instances, the males arrives at the breeding colony before the females, and begin building their nests. Once the females have arrived though, both birds will often still do some nest building and maintenance. And there does seem to be a bonding aspect of presenting the rock to the mate – it is often accompanied by head bowing and shaking, as well as vocalizing – which are all bonding behaviors.
DeNapoli confirmed that rocks are frequently gifted to mates but again didn't mention the lengthy "perfect rock" search central to the penguin courtship rumor. Courtship has been observed in penguins, but typically pebble presentation is not a significant part of it: "Once a female chooses her mate, the pair will go through an important courtship ritual, in which the penguins bow, preen and call to each other. The ritual helps the birds get to know one another, and learn their respective calls so that they can always find each other."
A 2013 Slate animal blog post examined whether the same Adélie penguins were some of the animal kingdom's most egregious sexual deviants, an observation similarly made through the lens of comparison with human habits:
Shocking behavior isn’t the sole province of marine mammals. One naturalist was so thoroughly disgusted with the sexual behaviors of Adélie penguins that his observations were hidden from view for almost a century.
Known as Pygoscelis adeliae to scientists ... the Adélie penguin was one of the subjects that caught the attention of scientist George Murray Levick while he ventured to the South Pole with the 1910-13 Scott Antarctic Expedition ... the species shocked and horrified Levick so much so that his four-page report “Sexual Habits of the Adélie Penguin” was purposefully omitted from the official expedition findings and distributed only to a small group of researchers considered learned and discreet enough to handle the graphic content.
While visiting Adélie penguins rookeries, Levick was shocked by the activities of what he called “hooligan cocks.” Males accosted and copulated with other males, females that were injured, chicks that had tumbled from their nests, and corpses. In desperation, some male Adélie penguins tried to mate with the ground until they ejaculated. Levick recorded these behaviors as aberrations from the norm of nature. “There seems to be no crime too low for these penguins,” he confided to his journal.
Later researchers rediscovered what Levick had seen. Rather than being deviant, the behaviors were a regular part of penguin life, triggered by males associating a rather flexible interpretation of a female’s mating posture with receptiveness. As Natural History Museum, London ornithologist Douglas Russell and colleagues reported in a preface to Levick’s belatedly-released report, this behavior is so ingrained that when a researcher set out a dead penguin that had been frozen in such a position, many males found the corpse “irresistible.” In a bit of weird field work, the same researcher found that “just the frozen head of the penguin, with self-adhesive white O’s for eye rings, propped upright on wire with a large rock for a body, was sufficient stimulus for males to copulate and deposit sperm on the rock.”
As Douglas and colleagues stressed in their preface to Levick’s report, though, “the behavior [displayed by hooligan males] is clearly not analogous to necrophilia in the human context.” That fact can easily be lost when one is appalled by an animal acting out a human taboo. Levick was aghast because he viewed the penguins in human terms, as little gents and dames dressed to the nines, and applied sentiments about proper human behavior to the penguins (and vice versa). For if such awful displays occurred in nature, what might that say about our own actions?
Slate's rehash wasn't the only less-than-romantic take on penguins' sex lives. A 1998 BBC article suggested that not all penguin partner pebble exchanges were quite so romantic:
Penguins are turning to prostitution. But instead of doing it for money, Antarctic dolly-birds are turning tricks to get rocks off their menfolk ... Stones are essential for penguins to build their nests. A shortage has led to the unorthodox tactics.
"Stones are the valuable currency in penguin terms," said Dr Fiona Hunter, a researcher in the Zoology Department at Cambridge University, who has spent five years observing the birds' mating patterns ... Prostitution is described as the world's oldest profession. But Dr Hunter is convinced it is the first time it has been seen in animals.
All of the female penguins Dr Hunter observed trading sex for stones had partners ... Penguins stick to the same mate, she said, but none of the males twigged what was happening.
"There was no suspicion on the part of the males. Females quite often go off on their own to collect stones, so as far as the males are concerned there is no reason to suspect ... It tends to be females targeting single males, otherwise the partner female would beat the intruder up."
On some occasions the prostitute penguins trick the males. They carry out the elaborate courtship ritual, which usually leads to mating.
Having bagged their stone, they would then run off [Hunter] said she does not think the female penguins are doing it just for the stones.
"The female only takes one or two stones ... It takes hundreds to build the nest to get their eggs off the ground. I think what they are doing is having copulation for another reason and just taking the stones as well. We don't know exactly why, but they are using the males."
It's human nature to anthropomorphize animals, and penguins are no exception. However, while penguins courtships are perhaps less human than once thought, they are no less interesting for it. Penguins are often observed deviating from expected sexual norms and even purportedly trade pebbles for sexual favors, but the primary purpose of exchanging pebbles and stones between penguins involves physical construction of a nest and not "romance." And while female penguins may occasionally be picky about the nest-construction usefulness of certain proffered pebbles, that doesn't mean males regularly traverse entire beaches to ensure finding unspecified "perfect pebbles" for their beloved lady-penguins.