While I can't speak for Islam in broad terms, I can speak a little bit about Buddhism. Even then though, I had to think about it at first, because the idea paganism exists in far more fluid terms in the places where Buddhism is prominent vs Christian and Muslim places. Buddhism is in many was a cultural and religious sponge, being more compatible and requiring less "conversion" than your Abrahamic religion. For Buddhists, the key is not in a belief in gods or a creator, but rather in the Buddha and the teachings he left behind. Buddhist cosmology, while denying the existence of an absolute creator deity, accepts the existence of powerful beings, gods and spirits, and specifically mentions Mara, Yama, and Brahma in the Pali canon, Hindu deities that predate Buddhism by some 500-1000 years. From the very beginning Buddhist texts incorporate some Indian deities into their religion. Mahayana gives us even more examples, with saints and gods becoming Bodhisattva. As Buddhism spread, it soaked up regional gods and practices.
Here I'm going to zoom in on two separate traditions, Japanese Buddhism and Tibetan Buddhism. While both are descended in part from the Mahayana school (although the Tibetan school is often separated into Vajrayana or Esoteric Buddhism due to its practices being rather different from traditional Mahayana. In fact Japan has ties to the Esoteric form of Buddhism too, though it took on a very different role.) they could not be more different due to the ways in which the culture they were part of influenced them both.
Before we continue, I need to make an important distinction. You see, Shinto as we know it has only truly existed for 250 or so years. While not wholly a modern invention, it codified the Japanese religious tradition and fused it with a rigid worship of the Emperor as a living god and chief of the pantheon and stripped non-Japanese elements away in an attempt to create a purely "Japanese" tradition. That said, many primary practices, legends, symbols, and Kami date back to pre-Buddhist and even prehistoric (The first mentions of Japan are found in the first century CE and it isn't really until the late-third century where we have detailed information) times. When I'm talking about Shinto or Kami tradition here, I am refering to the general folk beliefs of Japan which differs in some ways, but is very similar in others, to the modern idea of Shinto.
Let's start with Japanese Buddhism for no other reason than it comes first alphabetically. Buddhism entered Japan officially in 552 CE but likely was there before that, probably a few decades earlier, but certainly no more than a century before. At this time the Japanese already had a flourishing Kami tradition which would later become known as Shinto. This presented a problem for the elite and ruling class who began to favor the Buddhism that was brought from Korea and China as the worship of Kami and the rituals associate with them would not simply end and were in many places antithetical to Buddhist doctrine. Regardless of the contradictions apparent in the two traditions, they were practiced side by side for the most part. With the introduction of Tendai, the role of Kami in Japanese Buddhism changed and many Japanese Buddhists followed the new idea that the Kami were spirits that helped bring enlightenment, allowing worship of both simultaneously without contradiction. While this was happening Buddhist Bodhisattva deities became identified as kami as well. Indeed Buddhism began to take a very important cultural role in society, dealing with death.
Death before Buddhism was a very different affair. The Japanese viewed it as unclean or impure so they often ritually cleaned themselves. In those days there were no or few formal priests for Shinto spiritual chiefs often led the community. Rather, Shamans were the link and communities performed the burial rites. Upon the arrival of Buddhism in Japan, communities became increasingly interested in how death could be avoided or at least stalled, the process of human souls becoming kami came into being and the early Buddhist exorcism rites began to come about. As the years went on, Buddhism became increasingly associated with death and funerary rites while Shinto became the celebration of life and death. Because of this, Buddhism became increasingly death-centered in Japan with the Esoteric forms becoming associated with the warrior monks, the extreme ascetics who mummified themselves alive, and the suicidal monks while the Mahayana forms gave us Amida Pure Land, Nichiren, and Jizo cults. The Esoteric forms largely died out but the Mahayana cults became an important part of Japanese culture with Jizo becoming a popular figure who was associated children and saving people from hell to take them to his Pure Land. Jizo is seen all over Japan even today, sitting on roadsides surrounded by dolls and offerings.
It was largely for this reason that Buddhism was able to survive repression in the days of Nobunaga and Hideyoshi (who favored Japanese Neo-Confuscim) and the Meiji Restoration (where State Shinto became the Nationalistic imperative). Now serving an important function, as much as the Meiji Government tried to split Buddhism from Shinto, the two were linked and nearly everyone practiced both to some degree. To this day, most Japanese practice both Buddhism and Shinto together with little distinction in between the practices. Those that are "Buddhist" often have Shinto influences and "Shinto" are tied deeply to Buddhist tradition. It actually makes it difficult to assess how many Buddhists there are in Japan because people will identify as both or either interchangeably though new movements like the Soka Gakkai are more Buddhist and less Shinto.
Onto Tibet. So Buddhism in the Land of Snows is kind of a big deal, so much so that perhaps 30% of the population were monks or worked in monasteries prior to the Chinese invasion and nearly the entire population was Buddhist. Tibetan Buddhism had spread as far as Europe and was the primary religion of Mongolia. It's a big deal. It was also far more esoteric than nearly all other forms of Buddhism, with mantras, yogic practice, and complex rituals alongside the traditional Buddhist meditation and study. Gods and demons stare out from walls and buildings and the very land itself seems to have a spirit. Tulkus, reincarnated teachers and incarnate Bodhisattvas, lead the monasteries and carry on the teachings of their past lives as incarnate Lamas. The rich and unique culture of Tibetan Buddhism takes many influences from the traditional religion of Tibet, Bon, so much so that they are incredibly hard to tell the difference between them.
Well, that isn't entirely true. Bon only really came about in the 14th century out of the folk traditions that were absorbed into Tibetan Buddhism and is in part a reconstruction of the animism and folk beliefs of pre-Buddhist Tibet. It can be hard to find the authentic bits of pre-Buddhist beliefs and the post-Buddhist beliefs in modern Bon, but lets look at some things that almost certainly are tied into the pre-Buddhist traditions.
The Tibetan creation myth details Chenrezig, the Buddhas disciple, begged him not to die his final death as the Tibetan land would have people and they would not reach enlightenment, but the Buddha made it Chenrezig's job to bring them to enlightenment. Chenrezig then gave a monkey, whose name I will not even try to pronouce or write down but it means something along the lines of "the Enlightened Old Monkey Father", enlightenment. One day, while Old Monkey Father was meditating a female demon seduced him and thus the Tibetan people were born. This origin myth likely predates Buddhism and was incorporated into the tradition later on with the addition of Bodhisattvas (I seem to recall hearing a version where the demon was an incarnation of Tara).
There are other practices too, many of the demons and Bodhisattvas unique to Tibet are adaptations of traditional deities from the pre-Buddhist times and creatures like the Gyalpo are the realm of Buddhist monks and Lamas to dispel. Indeed the role of Lamas as astrologers, mystics, and seers is a role that dates back to the pre-Buddhist priests (who were actually called Bon) and their mystical powers come from ancient Tibetan beliefs indicated by the early descriptions in ancient Chinese sources.
It is a little harder to find information on the pre-Buddhist myths of Tibet since they didn't write anything down prior to Buddhism, in fact Buddhism was the impetus for a Tibetan writing system, one developed entirely separate from Chinese script to have an exact translation for each Sanskrit word. Peeling back the edges of Tibetan Buddhism, however, gives us an interesting look at how deeply the Buddhists of Tibet fused their own myths, and those of the tantric Hindus, into the religion.