I would prefer not to discuss it here as I regard the Blessed Virgin Mary as the holiest of humans conceived with a human father, and I don’t wish to see any criticism of her or the prayers I offer thereof. If you are sincerely interested in learning about Marian devotion and what constitutes an appropriate prayer to the Theotokos, please PM me.
I must stress that we do not worship Our Lady; we venerate her, indeed, we venerate her more than anyone else, but we do not offer worship or adoration, which is an important distinction, for these are due only to God, and the Blessed Virgin recognizes that.
Now, there are some cults that actually worshipped Mary, or continue to do so. Two spring to mind: the fourth century Collyridians, documented by St. Epiphanius of Salamis in his fourth century encyclopedia of heresies, the Panarion, or Medicine Chest. That group is obviously long extinct, but more recently there is a group that appeared in the 1970s in Spain at El Palmar de Troya, the Christian Palmarian Church of the Carmelites of the Holy Face, also known as the Palmarian Catholic Church. Initially, they were a group associated with the Traditional Latin Mass, and believed based on visions by one of their two cofounders that Pope Paul VI was being held captive and had been replaced by an impersonator.
The madness got worse however, when the “visionary” declared himself Pope Gregory XVII, and began departing substantially from normative Christian doctrine, while imposing a strict cult condition and exploiting members for free labor. Meanwhile, again, due to revelations, he declared that the Blessed Virgin Mary is also present in the Eucharist, which is not the case in Roman Catholic, Orthodox or traditional Protestant theology (for example, that of the Lutherans, who do believe our Lord is physically present in the Eucharist). He also stripped the Mass down to an extremely brief, minimalistic service and ordained an extremely large number of bishops, each of whom had to serve mass at least daily, and despite its relatively large size, their ornate basillica in El Palmar de Troya would still have become cramped. The people in the cult became sleep deprived.
Later, he began working on rewriting the Bible to reinforce the bizarre Palmarian doctrines, before his death in 2004, when he was succeeded by Pope Peter II, who was succeeded around 2010 by a particularly nasty character, Pope Gregory XVIII, who later, to his credit, resigned, declaring the cult to be a fraud; their current primate is Pope Peter III.
The cult has become quite notorious in Europe, due to its financial exploitation of members and its practice of Scientology-style shunning. Fortunately, its membership has declined dramatically from what it once was, much like what has happened to Christian Science (which is far larger, and probably more dangerous, due to the fact that Christian Science teaches its members to avoid using doctors and medicine, and to instead pay a “Christian Science Practitioner” to pray for you. Jim Henson was raised in that cult, and while he did leave it, many believe it left in him a deeply ingrained fear of doctors, and this is believed to be the reason why he did not seek medical treatment for the sore throat (a strep infection) which would ultimately kill him at a tragically young age in the early 1990s.