I'm assuming here that you mean genuine existing cults and/or other religious bodies? The short answer: apparently so.
Note I said "apparently". For at least 3 decades, I've run into references to this or that cult springing up basing its belief systems on Lovecraft's works. Even Anton Szandon LaVey included references to HPL in The Satanic Bible and had two "Lovecraftian" rituals in his The Satanic Rituals (on which, horror and fantasy writers note: the rituals in this book are considerably more evocative than damn near anything I've run across in fiction where such rituals are concerned; I think LaVey was a charlatan, a carnie, and a bit of a nutter, but he could write very well when it came to this sort of thing; studying his examples might help improve on those created rituals writers include in their on fiction). However, I've yet to see any hard evidence of such cults (as opposed to individuals, some of whom I've met), with one major exception: The Esoteric Order of Dagon does exist, it does have a website (there are several devoted to different E.O.D.'s -- the original Esoteric Order of Dagon was an amateur press organization devoted to studying Lovecraft's literature from critical perspectives, as well as broadening out into fantasy -- especially dark fantasy -- in general; they are still ongoing, I believe; but look and you'll find the religious site as well). In fact, they posted on Sean Hannity's site at one time, causing a bit of a roil, as Sean responded to them as a surviving ancient Middle Eastern religion -- some of the comments were very amusing on all sides; mostly very intelligent, but amusing nonetheless. I discovered this when doing the very search for Lovecraft commentary that led me to this site back in early May.
How seriously to take this EOD, I don't know. From what little I've seen, and the fact that Daniel Harms et al. actually devote space to debunking it in their book on Lovecraft's Necronomicon -- which I really need to pick up, as I hear it's an interesting, level-headed, and very well-researched book indeed (titled The Necronomicon Papers, if I remember correctly) -- they are actually quite sincere. However, from the bits of their literature I've seen, they're hardly the "evil cult" type, much more New Age-ish than anything. As I said, I haven't really looked into them in depth, but that's the impression I've received from what I have read.
There have been a few scattered individuals who took this stuff seriously, all the way back to a correspondent of HPL's called William Lumley, who lived in upstate New York, and who was convinced that HPL, REH, CAS, & Co. were all actually mouthpieces for these gods that existed, whether they knew it or not. Lovecraft was a bit taken aback (not to mention amused) at all this, but had no luck persuading Lumley of the fallaciousness of the notion. He even revised (read: rewrote) a story for Lumley, "The Diary of Alonzo Typer", available in The Horror in the Museum and Other Revisions from Arkham House, should you be interested.
So, apparently such cults exist, and certainly some individuals do; but there are no truly widespread secret organizations that have come to light (and, despite the term "secret organization", it's very difficult to have a widespread religious organization of any type that doesn't leak out in this day and age, at least to some intelligence agency, whether or not the general public ever become aware of them).
To be perfectly frank, part of this can be laid to HPL's own doorstep for writing about this stuff with, as he put it, the verisimilitude of an actual hoax, in order to increase the believability for the reader's suspension of disbelief. I think sometimes he gave too much credence to the scepticism of the average reader about such matters; but he also took this approach for his own aesthetic gratification -- look at the thickness of the historical feel (a blend of both created and quite genuine history) to his work, hinting that there are certain areas of history of which we either know little or nothing, or of which we see one thing, but what lies behind it is something much, much darker. Some excellent examples of this lie in his blending of genuine Providence and Rhode Island history in "The Shunned House" and The Case of Charles Dexter Ward, almost inextricably intertwined with genuine history, such as the 1890s exhumation, beheading and staking of a corpse to prevent vampiric attacks which was how rustics in the Nooseneck Hill region interpreted an outbreak of what was then still often called "consumption" (i.e., tuberculosis or tuberculor pneumonia) -- this is genuine history, cited in newspapers and books on R.I. history, and you can find more on this on various websites, including graphs showing the incidence of consumption and various other things connected to it. "Vampirism in Rhode Island" is the article, I believe, which is easiest to find. But the upshot of all this is that no few people took this stuff seriously -- Robert E. Howard did at first, until HPL disillusioned him, then he joined in the game -- even back when the stories were published in Weird Tales, Astounding and Amazing Stories. This is evident from various letters sent to "The Eyrie", WT's letters column, asking for more information on these secret societies and the ancient tomes so often cited in the stories.
Anyway, that's the longer version of the short answer above. Hope you find it interesting -- I kept even this extremely short, as several books have been written on the subject, it would seem, both (at least semi-)serious occultism and outright parody, as well as some genuine scholarship tackling the issue.
