Europe:
The pre-Christian religions in Europe were polytheistic religions. The Greek philosophers and poets were mostly rational, but they also sought a deeper connection with the whole, the “Unio Mystica”. Well-known representatives are Heraclitus (“Pantha Rei”, “You can’t step into the same river twice!”), Pythagoras, and especially Socrates.
Before the polytheists, people lived in tribes and hordes in which the shamans sought and mediated harmony with nature, also for hunting luck and survival. The best-known representative is probably Miraculix.

And then Christianity in Europe (and America) produced mystics and mystical movements: Francis of Assisi, Hildegard of Bingen, the Charismatic Church.

Middle East, North Africa:

In Islam, we know the mystical orders of the Sufis, the dervishes. They turn on their own axis, chanting the name of Allah. Islam is a religion in which mysticism has always played a major role. Well-known Sufi poets and mystics: Rumi, Attar, Hafiz.

South Asia:

India is a country where the mystics, the saddhus, can still be found in the temples and on the streets today. Hinduism is a very mystical religion with a lot of ecstasy and worship of the gods.

Tantra is a movement that flourished around the year 1000 and is known for the mystical experience of sexual ecstasy (certainly only a secondary aspect of tantric teachings).
East Asia:

Buddhism is a rather rational, analytically thinking philosophy and world doctrine that originated in India. But in its Zen Buddhist direction, founded by Bodhidharma in China and further developed in Japan and Korea in particular, it is now one of the leading mystical teachings worldwide. Zen conveys a direct experience of the essence of this world.

In China, Taoism, the mystical counterpart to Confucianism, contributed significantly to the development of Zen Buddhism. The works of the great Taoists, such as Lao-Tse and Chuang-Tse, are read worldwide today. The Tao-Te-Ching is one of the greatest books for many people.

America, Australia:

Did indigenous peoples have mystics? No question, because the shaman played a major role in every tribe. But there were also important religious founders such as Tecumseh (or his brother) or Handsome Lake.

Africa:

“Animistic nature religions”. Voodoo. Rhythm is lived mysticism.