Many readers have noted similarities between Celtic and British mythology and J.K. Rowling's fantastical magical world. When talking about this connection in terms of the Horcuxes, I'd like to focus on British mythology, specifically the myths and legends of King Arthur.
One of the most obvious connections between Arthurian myth and Horcruxes does not actually involve a specific Horcrux, but a method of destroying Horcruxes. Gryffindor's sword has the power to destroy Horcruxes, and this magical weapon parallels Arthur's famous weapon, Excalibur, which is drawn from a stone in the same way Gryffindor's sword can be drawn out of the Sorting Hat. Similarly, Hufflepuff's Cup, an actual Horcrux, can be seen as analogous to the Holy Grail, an important object in Arthurian myth. Finally, just as Dumbledore's destruction of the ring Horcrux ultimately leads to his death, in Arthurian myth Merlin receives a ring which later leads to his imprisonment (sometimes in a tomb, according to some versions of the legend).
As you can see, there are many parallels between British mythology and the Horcruxes. However, these connections don't even begin to cover the extensive allusions to myth and legend that can be found in Rowling's work. This is one of the many qualities that makes the original Harry Potter novels so enduring.