The four greatest Chinese legends are: the Butterfly Lovers, Madame White Snake, the Weaving Maid and the Cowherd, and Mengjiangnu.
1. The Butterfly Lovers
Among these four legends, this one is the most popular.
What Wikipedia says about the Butterfly Lovers:
The story is set in the Eastern Jin Dynasty.
A young woman named Zhu Yingtai from Shangyu, Zhejiang, disguised herself as a man travelling to Hangzhou to study. During her journey, she met and joined Liang Shanbo, a companion schoolmate from Kuaiji (會稽, Kuàijī, now known as Shaoxing) in the same province. They studied together for three years, during which their relationship strengthened. When the two parted, Zhu offered to arrange for Liang to marry her 16 year-old fictitious sister. When Liang travelled to Zhu's home, he discovered her true gender. Although they were devoted and passionate about each other at that point, Zhu was already engaged with Ma Wencai (馬文才, Mǎ Wéncái), a man her parents had arranged for her to be married to. Depressed, Liang died in office as a county magistrate. On the day Zhu was to be married to Ma, whirlwinds prevented the wedding procession from escorting Zhu beyond Liang's tomb. Zhu left the procession to pay her respects for Liang. Liang's tomb split apart, and Zhu dived into it to join him. A pair of butterflies emerged from the tomb and flew away.
This story is regarded as the Chinese Romeo and Juliet. Operas, TV series, motion pictures, etc. have been based on this story. The music is as famous as, if not more famous than, the story itself. The story inspired the production of Butterfly Lovers' Violin Concerto, or Liang Zhu Violin Concerto as known in Chinese. Then the music is played in all kinds of traditional Chinese instruments. Many foreign artists have also performed the music:
Richard Clayderman plays the Butterfly Lovers on December 27, 2005 (his Romantic Piano 2006 New Year Concert) in the Great Hall of the People in Beijing, China
Kenny G plays the Butterfly Lovers on October 11, 2007 for the closing ceremony of the 2007 Special Olympics World Summer Games in Shanghai, China
It is said that this music has been played in the space to contact with the aliens. I recall that I have read about this news somewhere before, but I cannot verify the source at the moment.
2. The Legend of the White Snake
The legend of white snake is a beautiful and moving folktale. It tells how the fairy maiden Bai Suzhen struggles against the rascally monk Fa Hai, the representative of the reactionary feudal forces, in her pursuit of freedoms and happiness, reflecting the sharp conflict between the common people and feudal ruling classes. In this story we see the people's yearning for freedom and their ever-defiant stand against the oppressive forces of feudalism.
The story has evolved over a period of about hundreds of years. Textual research indicates that it first appeared in the Song dynast (960-1279) story-tellers' prompt book the Legend of the three Tower by the West Lake.
3.The Weaving Maid and the Cowherd
What China Daily says about the Weaving Maid and the Cowherd:
As the story goes, once there was a cowherd, Niulang, who lived with his elder brother and sister-in-law. But she disliked and abused him, and the boy was forced to leave home with only an old cow for company.
The cow, however, was a former god who had violated imperial rules and was sent to earth in bovine form.
One day the cow led Niulang to a lake where fairies took a bath on earth. Among them was Zhinu, the most beautiful fairy and a skilled seamstress.
The two fell in love at first sight and were soon married. They had a son and daughter and their happy life was held up as an example for hundreds of years in China.
Yet in the eyes of the Jade Emperor, the Supreme Deity in Taoism, marriage between a mortal and fairy was strictly forbidden. He sent the empress to fetch Zhinu.
Niulang grew desperate when he discovered Zhinu had been taken back to heaven. Driven by Niulang's misery, the cow told him to turn its hide into a pair of shoes after it died.
The magic shoes whisked Niulang, who carried his two children in baskets strung from a shoulder pole, off on a chase after the empress.
The pursuit enraged the empress, who took her hairpin and slashed it across the sky creating the Milky Way which separated husband from wife.
But all was not lost as magpies, moved by their love and devotion, formed a bridge across the Milky Way to reunite the family.
Even the Jade Emperor was touched, and allowed Niulang and Zhinu to meet once a year on the seventh night of the seventh month.
This is how Qixi came to be. The festival can be traced back to the Han Dynasty (206 BC-AD 220).
Traditionally, people would look up at the sky and find a bright star in the constellation Aquila as well as the star Vega, which are identified as Niulang and Zhinu.
The two stars shine on opposite sides of the Milky Way.
This is how Qixi, or the Double Seventh Festival, sometimes also called the Chinese Valentine's Day, which falls on the seventh day of the seventh lunar month, came to be.
4. Mengjianu / Lady Mengjiang
Mengjiangnu lived in the Qin Dynasty (221-206BC). At the night of her wedding, her husband was taken away by the government troops to join in the Great Wall construction. A year later, Mengjiangnu went all the way to take some warm clothes to her husband. When she got to the Great Wall, she was told that her husband had died and had been buried under the Great Wall. Mengjianu started to wail, and the Great Wall began to collapse. At last, he spotted her husband's corpse.
Of all the four legends, I am most uncertain about the details of this one. If you are interesed in this one, you can read this article
for more details.