Creating Life Is Unforeseen

The Professor has some really cool experiment going on. Probably involving biology, computers, or something like that. The result is indeed cool. In fact, it's so cool that it has the unforeseen side-effect of being an actual person. Whoops!

This new person or species is benevolent, and quite obviously worthy of human rights. Obvious to the audience, that is. The creators might fail to understand this, thus causing all kinds of trouble. However, in some cases, rejection from the creators may lead the created character to resentment or worse.

If this trope leads to Deity of Human Origin, expect it to come with a dose of God Is Flawed. Contrast Playing God and Creating Life Is Awesome, where creating sentient life was the goal.

Supertrope of Instant AI, Just Add Water and It Came From the Fridge: If the unforeseen intelligence is technological or culinary in nature, see that trope instead. Examples of ambiguous nature goes on both pages.

Anime and Manga

 * The accidental creation of "Saati" in A.I. Love You.

Comic Books

 * In the Lucifer chapter The Yahweh Dance, creates a new universe as a part of training to be a good God. While a carefully monitored intelligent species arises, these events distracts this new and inexperienced God to overlook another continent, and the sentient species evolving there. The rest of the plot is spent by God trying to stop the chosen people from slaughtering this other people in God's name.

Fan Works

 * A zig-zagged example can be found in No Longer Than Thy Love, the final installment in Richard Lawson's seminal All-Purpose Cultural Cat Girl Nuku Nuku fanfic cycle from the late 1990s. In it, Nuku Nuku's "little brother" Ryunosuke, now an adult in his thirties, has spent years trying to create an AI that will replicate the mind and personality of his deceased "sister".  He finally decides that the simulation neither really succeeds nor passes the Turing Test, but before he can erase it, the AI realizes it is in danger and transfers itself to an android body.  In coping with its new hardware and the overwhelming range of sensory input it offers, the A.I. finally makes the jump to true personhood -- something it then takes a potential crisis to convince Ryunosuke of.

Film

 * In Tron: Legacy, Flynn creates life on purpose, and all is well. But then his actions cause a new species to evolve...

Literature

 * In the Cthulhu Mythos, Azathoth created reality itself by accident.

Multiple Media

 * The entire point behind the Bionicle story was that Mata Nui, AKA a planet-sized space-robot whose body houses the Matoran Universe, was meant to function as a sentient but "lifeless" robot, along with everyone living inside him. Instead, they built up cultures, began worshiping Mata Nui as a deity, developed relationships, formed alliances, fought wars... Sadly, this didn't prevent another creation of the Great Beings, Marendar, from seeing them as more than just robots, and began to carry out his task of shutting them off. Well, "slaughtering" would be a more fitting expression.

Tabletop Games

 * In Scarred Lands, the Titan Thulkas often create entire species, sometimes sentient ones, without even noticing. Goblins and giants are among his creations. It is implied that the humans are as well, since they was created before the Gods (thus by the Titans) but nobody know for sure by whom, and none of the titans clame credit for the deed.

Web Comics

 * Jyrras of Dan and Mab's Furry Adventures created two different lifeforms, both by accident.

Real Life

 * Science isn't quite there yet. But in 1952, researchers Stanley Miller and Harold Urey of the University of Chicago set up conditions thought to be similar to those of primordial Earth and observed spontaneous synthesis of amino acids and RNA.