The golem everyone knows, made of Vltava clay by Rabbi Judah Loew ben Bezalel, the Maharal of Prague, to defend the Jewish quarter against blood-libel accusations, animated by a name of God on a slip of paper or the word emet on its forehead, deactivated by erasing the first letter to leave met, dead, and stored in the attic of the Old-New Synagogue, is a real and important story that is not a medieval one.
Judah Loew was a genuine and eminent figure who died in 1609. Nothing written in his lifetime, and nothing written for two centuries afterwards, connects him to a golem. He does not mention it; his contemporaries do not mention it; his own extensive writings, which are about other things entirely, are silent.
The legend appears in print in the nineteenth century. Earlier golem stories had attached to other rabbis, notably Elijah of Chelm in the sixteenth century, and the Prague attribution appears to be a transfer. A collection published in 1909 by Yudl Rosenberg, presented as a rediscovered manuscript by Loew's son-in-law, gave the story its full and now standard form; it is generally regarded as Rosenberg's own composition.
That does not make the story worthless, it makes it a modern Jewish response to modern Jewish circumstances, written when blood libels were still being prosecuted in eastern Europe. Gershom Scholem treated the golem tradition as a serious strand of Jewish mysticism and the Prague legend as its folkloric flowering.
Its influence outside Judaism is large. The golem stands behind Frankenstein's creature in the popular imagination, behind the word robot, coined by a Czech writer in 1920, and behind most subsequent stories about a made thing that will not stop.