The so-called Mask of Agamemnon
Before late in the 19th century, most scholars thought that the Trojan War was pure myth. But one true believer, the rich German-American businessman turned amateur archaeologist, Heinrich Schliemann, found evidence for Bronze Age Greece and convinced many that there really was a Trojan War. Starting in 1871, he dug at Troy, where he uncovered a rich (but rather small) city; he then dug at Mycenae, where he found further rich remains, including a set of funeral masks in a circle of graves within the citadel walls ("Grave circle A"). Schliemann was convinced that the mask above, because of its nobility, must be that of Agamemnon; he is said to have telegraphed the king of Greece "I have gazed upon the face of Agamemnon."
Unfortunately the grave dates from around 1600 BC, far too early for the hero of the Trojan War, which would have taken place sometime around 1200. Schliemann was in fact something of a charlatan, but the sort of energy and romantic dreaming he provided are often necessary to move more traditional scholars forward. The masks below show rather less noble looking masks from the same set of graves.
So was the Trojan war historical? Was there really a historical Agamemnon, Odysseus, and the rest? Maybe--but only in the vague sense that it remains possible that Mycenaean Greeks destroyed Troy sometime around 1200 BC. For more on the historicity of the Trojan War, check out Jeremy Rutter's Lesson 27.
For more on the shaft graves, check out Jeremy Rutter's Lesson 16.

Rather less noble looking inhabitants of Grave Circle A at Mycenae.