"Frankenstein" breaks many rules of the genre. The legend of its genesis is known, what some people forget is that in that night in Switzerland, where famous intellectuals (P.B.Shelley, Byron) almost challenged those they reputed inferior (M.Shelley, William Polidori), Polidori, Byron's assistant, himself wrote "The Vampire", clearly inspired to his "boss", and basically having already in it most of the features of Stoker's "Dracula" (extremely charming person, the person who drains the life energy of the others): we know a bit of the myth of the Byronic hero.
Let's go back to "Frankenstein". There is no clear hero or clear villain: the doctor and the monster are both, at different stages of their story. The setting is no more some ancient backwater place, but advanced Switzerland (mostly), not a middle ages Catholic country but a modern Calvinist one (and Calvinism being the main source for Puritans, see above). Dark and light mingle, we (and probably also M.Shelley's audience) sometimes feel unease yet enthusiastic about the Doctor's hubris. He is a hero, but he is overeaching and as the characters of the myths (Prometheus, Icarus) the higher the fly the sounder they fall. He challenges the basic law of nature, he tries to replace God's role in life and death. But as Blue stated, this book is also the probable ancestor of science fiction. Yes, because we must not forget Gothic novel, as a genre, reacted against Enlightment. So, on a more narrow sighted level, we could consider it also as a simple allegory on the danger of science.
So, M.Shelley showed you didn't need specific schemes in characters, and their own development was part of the pleasure of reading; she showed you didn't need ancient places, or imaginary settings, you could use the here and now; she showed that a message, not necessarily a Puritan or religious message, could be conveyed allegorically. It could still entertain you, and show darkness and light, evil and good, in struggle, and even more confusionary struggle. She paved a possible way.
Gothic novel in the 19th century had a more complex life and development. On a side, it got back to its own origins, that is a more schematic and entertaining aimed genre. Even then, a book such as "Wuthering Heights" by E.Bronte is considered one of the masterpieces of novel in genre, and actually it is: yet it is definitely and quintessensially gothic, for its irrational passions leading to damnation, for the ghosts, for the atmosphere: "I am Heathcliff" says poor Catherine shortly after she has caused with her choice her own fall along that of Heathcliff himself. But Victorian novel became a sort of institution, and still you needed to convey a moral message if you wanted to be considered a serious writer, and not just the writer of "rubbish". People were slightly more literate, there had been reforms, and had more free time, literature of evasion and entertainment was widespread, because most people, even if they could read, could not face too difficult or complex works. Gothic didn't die: there are many gothic elements in Dickens, one of the most typical Victorian writers, you just need to think about discomforting Miss Havisham in "Great Expectations", or the world-wide-known "Christmas Carol".
Some writers, especially in the late Victorian period, experimented the use of proper Gothic novel as an allegory, more or less as M.Shelley had done. I won't reduce "Dracula" to a criticism of colonialism, nor "Doctor Jeckil and Mister Hyde" to a criticism of the double façade of Victorians, but we cannot deny there are elements of this too. Good and evil becomes shaded, as they were in "Frankenstein", as they were in "Wuthering Heights", it becomes matter of obsession, lust, strong passions, and, above all, of choices. And the century closes with Oscar Wilde's "The Picture of Dorian Gray", which, to some extent, has all those things too, and was written by a person who normally worked for bourgeoise theatre and was known for his witty conversations.
Unfortunately my own knowledge on 1900 gothic novels is limited. I could say more on previous periods, but more or less this is the development of the genre. Once I may waste some time of mine and trying to approach things such as "Twilight" and "Vampire's Diaries", but I fear they come more from the development of romance (and mind, things such as "Wuthering Heights" can be inserted there too) than of proper gothic. Plus, I've completely overlooked, at this stage, all the influence of science fiction, fantasy, translations of Grimm Brothers' tales, which to some extent also influence "culture", in general, of the Victorian period. I've also ignored all the development of American gothic (Irving, Hawthorne, Poe, H.James) which had a strong influence later, and unfortunately my own Ph.D. is just in Literature of English Speaking Countries, so not enough lore on other countries (though I may add "Pinocchio" has several gothic elements, some Hugo's works, Gogol, Kafka, etc)
