Greatest Plays of All Time

CLASSICAL GREECE & ROME

Persians, by Aeschylus (472 BCE)
Empathy with the defeated enemy
Antigone, by Sophocles (441 BCE)
The necessary allowance of civil disobedience
Electra, by Sophocles (420-414 BCE)
The terrible infinity of revenge
Medea, by Euripides (431 BCE)
The horrific destructiveness of spurned love
Helen, by Euripides (412 BCE)
The emptiness and futility of war
Lysistrata, by Aristophanes (411 BCE)
A sex strike against husbands who can't stop fighting wars
The Brothers Menaechmus, by Plautus (200 BCE)
Twinned similarities breed confusion

TRADITIONAL INDIA
Shakuntala, by Kalidasa (4th c. CE)
Lyrical play about love by India's greatest classical poet

TRADITIONAL CHINA
Injustice to Dou E, by Guan Hanqing (c. 1241/50-1320/24)
Fierce indictment of injustice and the powerless position of women
The Record of the Chalk Circle, by Li Xingdao (c. 1264-94)
In his judgement about a child, Judge Bao shows King Solomon's wisdom
Rain on the Wutong Tree, by Bai Pu (1226-after 1307)
Fatal infatuation of an aging emperor for a beautiful concubine
A Lone Goose in Autumn over the Palaces of Han, by Ma Zhiyuan (1250-1321)
Imperial concubine Wang Zhaojun married to a barbarian khan
The Story of the Western Wing, by Wang Shifu (1250-?1337)
China's most famous love comedy
Peony Pavilion, by Tang Xianzu (1598)
Girl who dies dreaming of a lover returns in spirit form - the Chinese "Romeo and Juliet"

TRADITIONAL JAPAN
Takasago (Group I, "god play"), by Zeami (1363-1443)
A very auspicious story, involving a loving and long-married couple
Atsumori (Group II, "warrior play"), by Zeami
Warrior renounces violence after cruelly killing a young flute player
Matsukaze (Group III, "woman play"), by Zeami
Ghostly attachment to a noble poet by two salt-making sisters
Sotoba Komachi (Group IV "aged woman"), by Kan'ami
Japan's greatest beauty, now old and poor, finds enlightenment
Kurozuka / Adachigahara (Group V "demon play"), author unknown
The story of a man-eating Onibaba "demon hag"
The Love Suicides at Sonezaki, by Chikamatsu (1703)
The true love of a courtesan
The Love Suicides at Amijima, by Chikamatsu (1721)
Chikamatsu's masterpiece about giri and ninjo
Kanadehon Chushingura (1748)
Archetypal story of the tormented lord and his loyal retainers
Tokaido Yotsuya Kaidan, by Tsuruya Nanboku IV (1825)
Japan's greatest horror story about the revenge of a slighted wife
The Subscription List (Kanjincho), by Namiki Gohei III (1840)
Benkei bluffs his way past the barrier checkpoint
Delicious Poison (Busu)
Two servants catch their master in a lie and silence him using his own logic

RENAISSANCE EUROPE
Romeo and Juliet, by Shakespeare (1597)
The archetypal love story
Twelfth Night, by Shakespeare (1599)
A cross-dressing young woman becomes entangled in a love triangle
Hamlet, by Shakespeare (1600)
Philosophical play about the ethical issues of murder and revenge
Measure for Measure, by Shakespeare (1604)
Macbeth, by Shakespeare (1605)
The Tempest, by Shakespeare (1610-11)
The Duchess of Malfi, by John Webster (c. 1613)
The Changeling, by Thomas Middleton & William Rowley (1622)
'Tis Pity She's a Whore, by John Ford (1629-33)
Punishment without Revenge, by Lope de Vega (1632)
Life is a Dream, by Calderon de la Barca (1635)
The Theatrical Illusion, by Corneille (1635)
Tartuffe, by Moliere (1664)
Attack on religious charlatanism and self-delusion
The Country Wife, by Wycherley (1675)
Phaedra, by Racine (1677)
The guilty love of a wife for her stepson leads to disaster

ENLIGHTENMENT EUROPE
Servant of Two Masters, by Goldoni (c. 1746)
Clever servant manages two masters at the same time
Minna von Barnheim, by Lessing (1767)
School for Scandal, by Sheridan (1777)
A rich uncle in disguise tests the worthiness of his nephews
Marriage of Figaro, by Beaumarchais (1778)

ROMANTIC EUROPE
Don Carlos, by Schiller (1787)
Turandot, by Schiller (1801, based on Gozzi 1762)
Egmont, by Goethe (1787)
Faust I, by Goethe (1808)
The Broken Jug, by Kleist (1808)
Woyzeck, by Büchner (1836)
The Government Inspector, by Nikolai Gogol (1836)
An incognito traveler is in a small town mistaken for an important official
A Month in the Country, by Turgenev (1848-50)
A married woman and her young ward both fall in love with a naive tutor
Italian Straw Hat, by Labiche (1851)

FIN DE SIECLE EUROPE
A Doll's House, by Ibsen (1879)
The awakening of a married woman who lacks opportunities for self-fulfillment
Hedda Gabler, by Ibsen (1890)
A newlywed struggles with a life devoid of excitement and enchantment
Miss Julie, by Strindberg (1888)
Bitter play about the battle between the sexes, made acute by class struggle
The Second Mrs. Tanqueray, by Pinero (1893)
A play about "a woman with a past"
Salomé, by Oscar Wilde (1891)
Fin de siecle decadence in deliciously ornate language
The Importance of Being Earnest, by Oscar Wilde (1895)
Satire and witty dialogues expose the superficiality of Victorian society
Uncle Vanya, by Chekhov (1897)
The Cherry Orchard, by Chekhov (1903-04)
A Flea in her Ear, by Feydeau (1907)
Lulu Plays (Earth Spirit & Pandora's Box), by Wedekind (1895-1902)
Dangerous femme-fatale leaves a trail of death and suicide
Reigen, by Schnitzler (1897)
Love keeps going round and round, until the snake bites in its own tail
Professor Bernardi, by Schnitzler (1912)
Clash between a medical doctor and a priest exposes antisemitism in Austria
Jedermann, by Hugo von Hofmannsthal (1911)
Morality play: God summons the rich bon viveur Jedermann
Mrs. Warren's Profession, by Shaw (1893)
A prostitute madam attempts to come to terms with her disapproving daughter
Pygmalion, by Shaw (1913)
Flower girl Eliza learns upper class manners but also finds independence

THE MODERN & CONTEMPORARY WORLD
Six Characters in Search of an Author, by Pirandello (1921)
Six characters abandoned by their author play out a family drama
Private Lives, by Coward (1930)
Tales from the Vienna Woods, by Horvath (1931)
European society in turmoil heading towards Fascism
Blood Wedding, by Lorca (1933)
Thunderstorm, by Cao Yu (1933)
Love between half-siblings in the complex family of an authoritarian patriarch
The Infernal Machine, by Cocteau (1934)
The Two Daughters of Mr Sawa, by Kishida Kunio (1935)
Murder in the Cathedral, by T.S. Eliot (1935)
Life of Galileo, by Bertolt Brecht (1938)
Long Day's Journey into Night, by O'Neill, (1940-01)
No Exit, by Sartre, (1944)
A Streetcar Named Desire, by Tennessee Williams (1947)
Fantasy world of fading southern belle shatters on harsh reality
Death of a Salesman, by Miller (1949)
Waiting for Godot, by Beckett (1953)
The Lady Aoi, by Mishima Yukio (1954)
Modern Noh play in which a possessing spirit kills her rival in love
Madame de Sade, by Mishima Yukio (1965)
Why the wife of the Marquis de Sade only left him after his release from prison
The Visit, by Durrenmatt (1956)
The Birthday Party, by Pinter (1957)
The Balcony, by Genet (1957)
Rhinoceros, by Ionesco (1959)
Who is Afraid of Virginia Woolf?, by Albee (1962)
Marat/Sade, by Peter Weiss (1964)
Friends, by Abe Kobo (1967)
Creepy play in which a weird family takes over the life of a lonely salaryman
La Marie-Vision, by Terayama Shuji (1968)
American Buffalo, by Mamet (1975)
Arcadia, by Tom Stoppard (1993)

When acquiring the plays, it is best to look for reliable publishers as Oxford World's Classics, Penguin and Penguin Classics, or one of the many university presses. These edition have excellent notes and introductions.

In the case of translations of non-English plays, I do not recommend to read the older translations which are in the public domain and freely available on Gutenberg.org or Wikisource, etc. - these translations are often in antiquated English or of questionable quality, and do not do justice to the original.

Books about plays:
Oxford Dictionary of Plays, Second Edition, by Michael Patterson (Kindle edition)
The 101 Greatest Plays from Antiquity to the Present, by Michael Billington (Faber & Faber, 2015)