This article accompanies the fable
The Golem has had an illustrious history ever since, well, the mid-19th century. Most of his history before that appears to be projections back in time - notably to late 16th century Prague where Rabbi Jehuda Loew ben Bezalel apparently first created one and stashed him in the attic of the synagogue. That's not to say the concept didn't exist before the mid-19th century - it did, dating back to the medieval alchemists and Jewish Kabbalists - but the fable about the Rabbi and the Golem protecting the Jews of Prague and smiting the anti-Semites seems to be more recent.
The Golem story really has its origins in the story of Adam - God takes a lump of earth and speaks the divine words, breathing life into it - Adam being the first Golem. It seems to be human nature to believe that life can be created in this way: magic spells and a hot breath on inanimate objects. No doubt the Venus of Willendorf, who is made of limestone even earlier, was similarly regarded.
In scientific terms this belief is related to Vitalism. It is hard to see science ever being able to deal with it satisfactorily since Vitalism relies on a magical or religious view of the world. I believe this reflects more on the limits of mechanistic science and the rigidity of many scientists rather than on the limits of religious belief. That said, the idea of infusing inanimate objects with life is not very persuasive.
Mary Shelley had her own take on the Golem fable in Frankenstein (1818) using electricity, influenced as she was more by Galvanism rather than Kabbalah. It also has been speculated by some that Tolkien's Gollum in The Lord of the Rings is a play on the name. Nowadays the Golem is
a Pokémon character and a potent means for attracting tourists to Prague. This upsets purists of course.