(or "The Sins Of The Father, Grandfather, Great-Great-Grand-Uncle, Et Cetera...")
When dealing with 'Frankenstein', it's important to carefully delineate which version of the Frankenstein mythos you're talking about in any given discussion. Because while they might all draw on the same source material, Mary Shelley's classic Gothic novel, they definitely don't have the same storytelling engine. The Hammer Frankenstein series, for example, followed Peter Cushing as Baron Frankenstein as he went through one diabolical experiment after another, descending ever further along a path of perfectly rational madness and calculating viciousness, until he turned into a monster far more inhuman than the ones he created.
The Universal Frankenstein films, though, took a far different tack. They started from virtually the same point: Frankenstein, a scientist with heretical views on artificial life, creates a human being out of an assemblage of corpses and animates it. The resultant Monster (which never gets a name, in the Universal canon) turns out to be a brutish, simple-minded beast instead of the perfect creation Frankenstein intended, at which point the drawbacks of making him eight feet tall with the strength of a dozen men become apparent.
The second Universal film is a pretty natural extension of the first, with Frankenstein being induced to make a female version of his creation (and in the process, creating the very first beehive hairdo.) But it's with "Son of Frankenstein" that the storytelling engine of the series really takes off, and the Frankenstein legacy becomes a key point of the series.
The third movie follows Frankenstein's now-grown son, Wolf, as he returns to his ancestral home, already interested in the reputation his father had and conflicted over his own views of his father as a brilliant man and a great scientist. Despite hearing about the horrors the Monster has visited on the village of Frankenstein over the decades (and yes, that's accurate--if he's the Baron von Frankenstein, it would make sense that the village is the village of Frankenstein), Wolf believes that his father's ideas were fundamentally sound...and when he discovers the dormant Monster, he decides to bring it back to life and cure its defects, fixing what his father made and showing the world what a genius his father truly was.
The first two movies are, of course, excellent cinema, but it's here that the series shows its true potential as a generational saga. This allows individual Frankensteins to progress along different character arcs--some redeeming themselves, some being destroyed, some taking the Hammer tack and becoming human monsters--while preserving the general theme of "scientist tries to do good, but creates evil." The Frankenstein Monster becomes a tangible symbol of a family secret, something that both repels and lures in successive generations of Frankensteins as it endures, eternally. It may fall into a pit of burning sulfur or get entombed in glacial ice, but it's always there, waiting for the next generation of Frankensteins to find and wonder about...and eventually bring to life once more.
Arguably, it's the abandonment of this theme, as much as anything else that led to the demise of the series (and there was quite a bit of "anything else", including random cast changes and a growing insistence on shoehorning in Dracula and the Wolf Man into the films.) And decades later, it was this theme that Mel Brooks returned to in his homage/parody "Young Frankenstein", a film that works as well at being a continuation of the Frankenstein story as it does at being a parody of the series. Frankenstein's grandson might do everything he can to deny his legacy, but, well, "Destiny, destiny, no escaping, that's for me!"
A reboot of this series might very well be warranted, in fact. If the original is set back at the time of Shelley's story, that gives writers a potential two hundred years of successive generations to play with, and all sorts of permutations to bring into the story. Perhaps a World War II era story, where a refugee Frankenstein works with the American government to make an atomic Monster? A Women's Lib Frankenstein who's tired of the lack of respect her female mad scientist ancestors have gotten? Frankenstein in the Great Depression, cobbling together a lab without the family resources? And at the back of it all, the original Monster, always there, always returning...it seems to be a storytelling engine ripe with possibilities, even beyond the ones already explored. And more than likely, it's one we'll see someday. Like its central character, people are always resurrecting the Frankenstein concept.