He's not mentioned in either the Iliad or the Odyssey. The reason for the omission that Susan Woodford* gives seems fair: The stain on the wily hero could never be effaced.
Although Homer doesn't mention this other clever Trojan War hero, the 3 major writers of Greek tragedy do, as does the author of the Cypria (part of the Trojan Cycle). Even Socrates does in Plato's Apology:
"What would not a man give if he might converse with Orpheus and Musaeus and Hesiod and Homer? Nay, if this be true, let me die again and again. I, too, shall have a wonderful interest in a place where I can converse with Palamedes, and Ajax the son of Telamon, and other heroes of old, who have suffered death through an unjust judgment; and there will be no small pleasure, as I think, in comparing my own sufferings with theirs."
In case you're still wondering his name, it's Palamedes. Palamedes was the one responsible for the trick that led to the drafting of Odysseus into the Trojan War. Here's what the Epitome of Apollodorus has to say about the event that led to Odysseus' dastardly deed of revenge:
[E.3.7] "But he, not wishing to go to the war, feigned madness. However, Palamedes, son of Nauplius, proved his madness to be fictitious; and when Ulysses pretended to rave, Palamedes followed him, and snatching Telemachus from Penelope's bosom, drew his sword as if he would kill him. And in his fear for the child Ulysses confessed that his madness was pretended, and he went to the war."
The following passage from the same work describes how Odysseus got revenge -- by framing Palamedes for treason:
[E.3.8] "Having taken a Phrygian prisoner, Ulysses compelled him to write a letter of treasonable purport ostensibly sent by Priam to Palamedes; and having buried gold in the quarters of Palamedes, he dropped the letter in the camp. Agamemnon read the letter, found the gold, and delivered up Palamedes to the allies to be stoned as a traitor."Learn more about the importance of Palamedes.
Image of Trojan War Heroes © Clipart.com.
* "Palamedes Seeks Revenge"
Susan Woodford
The Journal of Hellenic Studies, Vol. 114, (1994), pp. 164-169

Comments
Palamedes was great choice of topics. Too bad we don’t know other tales about him.
I was in Fairbanks, AK last week and saw a production of Antigone at the Fairbanks Shakespeare company. Wow! The director/writer painted the merest facade of modernity across the production and then stayes so true to the origional in spirit. (Including Antigone wearing a wedding gown in her tomb!) The performance was incredible particularly because the bulk of the cast were middle school girls! It says something about the quality of Greek literature that 2500 years later we are still performing and attending their plays.