He is believed to have written over ninety plays, eighteen of which have survived. It is now widely believed that a nineteenth, Rhesus, was probably not by Euripides (Ancient History Sourcebook). Fragments, some of them substantial, of most of the other plays also survive. More of his plays have survived than those of Aeschylus and Sophocles together, partly because of the chance preservation of a manuscript that was probably part of a complete collection of his works.
Euripides is known primarily for having reshaped the formal structure of traditional Attic tragedy by showing strong women characters and smart slaves, and by satirizing many heroes of Greek mythology.
His mother's name was Cleito, and his father's either Mnesarchus or Mnesarchides. Evidence suggests that Euripides' family was financially well off, and very influential. Due to this he was exposed to the great thinkers and philosophies of the day--including Protagoras Socrates, and Anaxagoras, who maintained that the sun was not a golden chariot steered across the sky by some elusive god, but rather a fiery mass of earth or stone. This exposure lead to his questioning of the religion he grew up with (It is recorded that he served as a cup-bearer for Apollo's dancers).
He had a wife named Melito, and together they had three sons. It is rumored that he also had a daughter, but she was killed after a rabid dog attacked her. Some call this rumor a joke made by Aristophanes, a comic writer who often poked fun at Euripides. However, many historians fail to see the humor in it, and believe that the story is indeed true.
The record of Euripides' public life, other than his involvement in dramatic competitions, is almost non-existent. It has been said that he travelled to Syracuse, Sicily, that he engaged in various public or political activities during his lifetime, and that he left Athens at the invitation of king Archelaus II and stayed with him in Macedonia after 408 BC; there is, however, no historical evidence for any of these claims.
Euripides first competed in the famous Athenian dramatic festival (the Dionysia) in 455 BC, one year after the death of Aeschylus. He came in third, because he refused to cater to the fancies of the Judges. It was not until 441 BC that he won first place, and over the course of his lifetime, Euripides claimed a mere four victories.
He was a frequent target of Aristophanes' humor. He appears as a character in The Acharnians, Thesmophoriazousae, and most memorably in The Frogs, where Dionysus travels to Hades to bring Euripides back from the dead. After a competition of poetry, Dionysus opts to bring Aeschylus instead.
Euripides' final competition in Athens was in 408 BC. Although there is a story that he left Athens embittered because of his defeats, there is no real evidence to support it. He died in 406 BC, probably in Athens or nearby, and not in Macedon, as some biographers repeatedly state. The Bacchae was performed after his death in 405 BC.
When compared with Aeschylus, who won thirteen times, and Sophocles, with eighteen victories, Euripides was the least honored, though not necessarily the least popular, of the three — at least in his lifetime. Later, in the 4th century BC, the dramas of Euripides became more popular than those of Aeschylus and Sophocles. His works influenced New Comedy and Roman drama, and were later idolized by the French classicists; his influence on drama reaches modern times.
In June 2005, classicists at Oxford University employed infrared technology – previously used for satellite imaging – to detect previously unknown material by Euripides in fragments of the Oxyrhynchus papyri,  a collection of ancient manuscripts held by the university. 
Tragedies of Euripides
- Alcestis (438 BC, second prize)
- Medea (431 BC, third prize)
- Heracleidae (c. 430 BC)
- Hippolytus (428 BC, first prize)
- Andromache (c. 425 BC)
- Hecuba (c. 424 BC)
- The Suppliants (c. 423 BC)
- Electra (c. 420 BC)
- Heracles (c. 416 BC)
- Trojan Women (415 BC, second prize)
- Iphigeneia in Tauris (c. 414 BC)
- Ion (c. 413 BC)
- Helen (412 BC)
- Phoenician Women (c. 410 BC, second prize)
- Orestes (408 BC)
- Bacchae and Iphigeneia at Aulis (405 BC, posthumous, first prize)
Fragmentary tragedies of Euripides
The following plays have come down to us today only in fragmentary form; some consist of only a handful of lines, but with some the fragments are extensive enough to allow tentative reconstruction: see Euripides: Selected Fragmentary Plays (Aris and Phillips 1995) ed. C. Collard, M.J. Cropp and K.H. Lee.
- Telephus (438 BC)
- Cretans (c. 435 BC)
- Stheneboea (before 429 BC)
- Bellerophon (c. 430 BC)
- Cresphontes (ca. 425 BC)
- Erechtheus (422 BC)
- Phaethon (c. 420 BC)
- Wise Melanippe (c. 420 BC)
- Alexandros (415 BC)
- Palamedes (415 BC)
- Sisyphus (415 BC)
- Captive Melanippe (412 BC)
- Andromeda (c. 410 BC)
- Antiope (c. 410 BC)
- Archelaus (c. 410 BC)
- Hypsipyle (c. 410 BC)
- Oedipus (c. 410 BC)
- Philoctetes (c. 410 BC)
- Cyclops (unknown)
- Rhesus (mid 4th century BC, probably not by Euripides, as maintained today by most scholars)
- Croally, N.T. Euripidean Polemic: The Trojan Women and the Function of Tragedy. Cambridge University Press, 1994.
- Ippolito, P. La vita di Euripide. N�poles: Dipartimento di Filologia Classica dell'Universit'a degli Studi di Napoli Federico II, 1999.
- Kovacs, D. Euripidea. Leiden: Brill, 1994.
- Lefkowitz, M.R. The Lives of the Greek Poets. London: Duckworth, 1981.
- Scullion, S. Euripides and Macedon, or the silence of the Frogs. The Classical Quarterly, Oxford, v. 53, n. 2, p. 389-400, 2003.
- Webster, T.B.L., The Tragedies of Euripides, Methuen, 1967.
- Encarta's entry for Euripides
- Euripides-related materials at the Perseus Digital Library
- Useful summaries of Euripides' life, works, and other relevant topics of interest at TheatreHistory.com.