the name that can be spoken is not the true Name.
Nothing can be said about the Tao/Dao. It's ineffable. So we can all go home, right?
To start with, it's sometimes considered a philosophy, and not a religion. However, there are many religious sects based off of Taoism. The line between philosophical and religious Taoism is very, very blurry. Philosophically, you can sum up Taoism thus: "Go with the flow." All problems in life come from going against the natural order of things. Passive virtue is superior to imposing your will, and poverty is better than great wealth. Taoism in its "pure" form is non-dualistic; both light and darkness (with neither good or evil alone), good and evil, active and passive qualities are contained within the eternal, flowing Tao.
Everything in the universe is made up from the flow of two equal, opposite, and interpenetrating forces. Yang is solid and masculine, represented by white in the traditional symbol you often see in martial arts movies. Yin, the feminine and passive quality, represented by black. When casting the traditional Yijing hexagram, Yang is solid yarrow sticks and Yin is broken sticks. From boundless nothingness (wuji) comes the duality of Yin/Yang, and from the duality comes "ten thousand things" as said in the Tao Te Ching (alternatively, Dao De Jing).
Of course nothing is really that simple. Taoism is deeply infused with Chinese animism and cultural beliefs. Taoism has a variety of sects with sweet names like "The Mighty Commonwealth of Orthodox Oneness" and "The School of Complete Reality." Many Taoist sects are deeply concerned with the individual soul, and are famed for discovering gunpowder in their pursuit of an alchemical elixir of immortality.
The foundational text of Taoism is the Tao Te Ching written by Laozi. Traditionally, it's been said he was a contemporary of Confucius's; modern research seems to indicate that either he lived in the Warring States Period (4th Century BCE) or he never existed. (So if he never existed, who would have written it? A compilation of various authors' works is the theory.)
Beyond all this, Taoism, like all Chinese religions, got liberally mixed up with Buddhism once it arrived in China in the sixth century CE. Most significantly, a Taoist philosopher of the Warring States period, Zhuangzi, was famous for telling parables and inventing koans. A few centuries later, Zhuangzi's style got mixed up with Mahayana Buddhist theology to create the school of Chán, known to the West by its Japanese name: Zen.
Offered for your edification is one of many translations of the Tao Te Ching. Other important texts include the Zhuangzi, which is best known in the west for the story about being a man-dreaming butterfly, or a butterfly-dreaming man. Taoist works have been collected and compiled together as the "Daozang" (Taoist Canon).
Of the traditional Chinese religions, Taoism has substantially higher appeal in the West than Confucianism, if only because the latter is so concerned with politeness and filial piety, whereas Taoism actually has things to say about spiritual matters. Possibly the most notable non-Chinese Taoist is Ursula K. Le Guin, who inserts Taoist themes into her works and has written a commentary about the Tao Te Ching.
- One episode of Cowboy Bebop has a girl who is a Taoist novice, going to the crew to have them help her find her father, an old friend of Jet's and a Tao master.
- Outlaw Star: The primary antagonists (as well as the Greater Scope Villains) are Space Pirate Tao masters, and their mastery gives them vaguely defined magical powers.
- A Chinese Ghost Story: One of the main characters is a reclusive Taoist wizard, who at one point has a musical number rapping about Taoism.
- Wooshi: A Korean movie about a Taoist wizard. It's a bit of a stretch as far as religious accuracy goes though, in all probability.
- In Kung Fu Panda, Master Oogway represents the Taoist philosophy, contrasting against his pupil Master Shifu's Confucianist discipline. Best exemplified in their exchange just before Oogway's passing, as they discuss how Po is to defeat Tai Lung:
Oogway: My friend, the panda will never fulfill his destiny, nor you yours, until you let go of the illusion of control.
Oogway: Yes. Look at this tree, Shifu. I cannot make it blossom when it suits me, nor make it bear fruit before its time.
Shifu: But there are things we can control! I can control when the fruit will fall. I can control where to plant the seed. That is no illusion, Master!
Oogway: Ah, yes. But no matter what you do, that seed will grow to be a peach tree. You may wish for an apple or an orange, but you will get a peach.
Shifu: But a peach cannot defeat Tai Lung!
Oogway: Maybe it can, if you are willing to guide it, to nurture it, to believe in it.
- Oracle of Tao: Strangely subverted. There is a Taoist temple, and many Taoist teachings. The subversion is that although this includes Taoism, it also includes Christianity, and a syncretic religion called Aiken. And some very strange cults, like the Church of the Holy Maple Tree.
- Shin Megami Tensei I: Tai Shang Lao Jun is the key representative of the Neutral path.
- Touhou Project: Following the 13th game in the series, a Taoist faction has become a part of the massive cast of mainstay characters. In a bit of a twist, these so-called "Taoists" do not practice either the religious or philosophical aspects of Taoism but only seek enlightenment in order to gain the powers that come with it. Ironically, the main character of the Touhou Project, local shrine maiden Reimu Hakurei, is in-universe noted as being more akin to a Taoistic hermit, both power and mentality-wise, than a Shinto shrine maiden.
- Taoism appears in the Crusader Kings II DLC Jade Dragon, followed mainly by Han Chinese characters, mostly the ones living in the "Western Protectorate" of the Chinese Empire, which exist in the eastern fringes of the map in the 769 A.D and 936 A.D start dates. It is a surprisingly good religion for stability and economic power, giving you bonus stewardship, no "Short reign" relations penalty with vassals, the ability to choose heirs, allows concubines and Taoist characters can choose between three "school of thought": Zhengyi Dao - the Way of Orthodox Unity, Quanzhen - School of Complete Perfection, and Shangqing - School of Supreme Clarity; It also makes it easier to "adopt Chinese imperialism" and form your own Imperial Dynasty. It should be noted that it comes with a dose of Artistic License Religion — Confucianism/Neo-Confucianism are absent, which is notable as the entire system of Chinese Meritocracy (which is present in-game) is based on its precepts. All Chinese characters are instead Taoist, so in-game Taoism also represents Confucianism to a certain degree.
- Taoism is back in Crusader Kings III but has been Demoted to Extra, there's only one start with Taoist rulers (867 A.D) and no province in the map follows Taoism. The religion has also been split into three separate faiths: Quanzhen, Shangqing and Zhengyi (the only one actually present at the start).