He joined the Greeks in the expedition against Troy. Pausanias in his Description of Greece (2.20.3) says that in Corinth is a Temple of Fortune in which Palamedes dedicated the dice that he had invented.
After Paris took Helen to Troy, Agamemnon sent Palamedes to Ithaca to retrieve Odysseus, who had promised to defend the marriage of Helen and Menelaus. Odysseus did not want to honor his oath, so he plowed his fields with an ass and an ox both hitched to the same plow, so the beasts of different sizes caused the plow to pull chaotically. Palamedes guessed what was happening and put Odysseus' son, Telemachus, in front of the plow. Odysseus stopped working and revealed his sanity.
The ancient sources show differences in regards to the details of how Palamedes met his death. 
Odysseus never forgave Palamedes for ruining his attempt to stay out of the Trojan War. When Palamedes advised the Greeks to return home, Odysseus hid gold in his tent and wrote a fake letter purportedly from Priam. The letter was found and the Greeks accused him of being a traitor. Palamedes was stoned to death by Odysseus and Diomedes. According to other accounts the two warriors drowned him during a fishing expedition. Still another version relates that he was lured into a well in search of treasure, and then was crushed by stones. Although he is a major character in some accounts of the Trojan War, Palamedes is not mentioned in Homer's Iliad.
Ovid discusses Palamedes' role in the Trojan War in the Metamorphoses. Palamedes' fate is described in Virgil's Aeneid. In the Apology, Plato describes Socrates as looking forward to speaking with Palamedes after death, and intimates in the Phaedrus that Palamedes authored a work on rhetoric. Euripides and many other dramatists have written dramas about his fate.
The three Fates created the first five vowels of the alphabet and the letters B and T. It is said that Palamedes, son of Nauplius invented the remaining eleven consonants. Then Hermes reduced these sounds to characters, showing wedge shapes because cranes fly in wedge formation and then carried the system from Greece to Egypt*. This was the Pelasgian alphabet, which Cadmus had later brought to Boeotia, then Evander of Arcadia, a Pelasgian, introduced into Italy, where his mother, Carmenta, formed the familiar fifteen characters of the Latin alphabet. Other consonants have since been added to the Greek alphabet. Alpha was the first of eighteen letters, because alphe means honor, and alphainein is to invent.
In one modern account, The Luck of Troy by Roger Lancelyn Green, Palamedes was double-dealing with the Trojans.
Defense of Palamedes is a text by Gorgias, describing the defense speech that Palamedes gave when charged with treason.
The major Dutch playwright Joost van den Vondel wrote in 1625 the play "Palamedes", based on the above Greek myth. The play had a clear topical political connotation, the unjust killing of Palamedes standing for the execution of the statesman Johan van Oldenbarnevelt six years earlier - which Vondel, like others in the Dutch Republic, considered a judicial murder. In Vondel's version, responsibility for the killing of Palamedes is attributed to mainly to Agamemnon; the play's harsh and tyrannical Agamemnon was clearly intended to portray Prince Maurits of Nassau. Authorities in Amsterdam found no difficulty in deciphering the political meanings behind Vondel's Classical allusions, and imposed a heavy fine on the playwright.
|Wikimedia Commons has media related to Palamedes.|