There are many accounts of the Buddha and his monks crossing paths with Nagas. The Buddhist Vinaya Piṭaka

Contents
Taming The Serpent
The Uruvelapāṭihāriyakathā
Throughout the night, the Naga brandished heat, fumes and fire against the Buddha. The Buddha however, remained unperturbed, easily outclassing the Naga in both flame and fury. Even after the serpent stood defeated, the Buddha continued to radiate a spectral glow of brilliant blues, reds, crimsons, yellows, and even the luminous brilliance of quartz. He subdued the Naga with ease, trapping him within his alms bowl.
At the end of the story, the Buddha also corrected the beliefs of Uruvela-Kassapa and his followers, who had earlier believed himself to be an Arahant like the Buddha. The Buddha showed them the err of their ways by sharing a sermon centred around fire, and how beings are trapped by their fires of clinging desire, aversion and delusion, leading to sorrow and despair. He explained how one can be released from such sorrow. At the end of the sermon, many of them attained Arahantship.
Battle Between Moggallana and A Naga King
Among his disciples with special capacities and qualities (A. I, 13), the Buddha often said that Moggallana
The Vissudhimagga
One day, while Nandopananda was enjoying a banquet surrounded by dancing female Nagas, he saw the Buddha, together with a retinue of monks, passing overhead to Tavatimsa

Several members of the Buddha’s retinue, including Ratthapála
Moggallana transformed himself into a larger Naga and coiled himself around Nandopananda, squeezing the life from out of the Naga king. In desperation, Nandopananda belched acrid smoke and fire to defend himself. The monk too unleashed his own smoke and fire, much to the Naga’s chagrin. Moggallana further tormented the Naga by shrinking himself and entering the Naga’s ears, nostrils and mouth, and even tickling his belly from the inside.
Enraged, the Naga king waited for Moggallana to exit from his mouth, and blew a tremendous blast of fire, intending to obliterate the monk. Try as he might however, blast after blast did not so much as singe a single hair on the monk’s body. The Naga king admitted defeat, and was brought to the presence of the Buddha, whereupon he sought refuge and tutelage instead.
Modern Day Encounters
In more recent times, stories still abound from people claiming to have encountered a Naga. Many of these accounts are from monks seeking spiritual attainment. During their tudong journeys through the wild, traversing mountain, jungles and caves, encounters with these mystical serpents were fairly commonplace. The following are accounts provided by Phra Ajarn Mun Bhuridatta

Nagas are said to enjoy listening to Buddhist sermons. He had preached to Nagas many times, and they often appeared to him in human form, both Male and Female. The serpents were particularly attentive, often asking deep spiritual questions, as they thoroughly invested in the Dhamma as a means of attaining a higher birth for themselves as humans.
This desire was borne of the Buddhist stipulation that only humans are optimized to carry out Dhamma practices and attain nibbana. Animals lack the facilities to achieve this. Even angels and deities cannot enter nibbana. Being reborn a human, is therefore considered the highest merit among Nagas.
At the time, Phra Ajarn Mun Bhuridatta was pursuing ascetic pilgrimage practices in a cave in Chiang Dao, Chiang Mai

When the Naga saw Phra Ajarn Mun Bhuridatta settle down in his territory, he began to scoff, and decided to interrupt him. At night, as Phra Ajarn Mun Bhuridatta moved about, the Naga became annoyed by the ruckus, and took every chance he could to lash out at the monk.
The serpent would reproach that the monk was stomping about and creating a huge din. It remarked that the sounds seemed like the running of a racehorse or the sound of sticks drumming upon the rock, vibrating throughout the mountains.
Each action Phra Ajarn Mun made was met with violent protest. Even though he was compassionate to the Naga, his compassion was met with disdain and turmoil.
He explained that to continuously find fault with others is to create endless sin for ourselves.
Afraid that this behaviour would accumulate more sin for the poor creature, Phra Ajarn Mun Bhuridatta began to preach the Dhamma to the serpent. The message of the sermon was one of self-reflection, and its importance in the face others’ faults.
Phra Ajarn Mun Bhuridatta explained that the habits of the past would continue to haunt the future, and should the Naga be fortunate enough to gain a human birth in future, he would often find himself in conflict with others due to his lack of forbearance. The slightest provocation or misunderstanding would result in chaos.
He explained that to continuously find fault with others is to create endless sin for ourselves. The Naga felt remorse for his actions, and resolved to mend his ways.

Phra Ajarn Mun Bhuridatta continued his Vipassana meditation in the cave for a while. He noticed that though the serpent had adjusted his habits, however the process appeared torturous to him. Worried that his meditation was imposing upon the Naga, he departed to continue on his journey.
These are just some of the modern-day accounts surrounding the Nagas. Stay tuned to our page for other forthcoming articles.
Sources of Reference:
https://www.accesstoinsight.org/lib/authors/nanamoli/index.html