An interesting thing about Neon Genesis Evangelion is that there are minor recurring details that sneak into several episodes in a small way before becoming obviously important in a later episode. One such artifact is the Spear of Longinus (sometimes referred to as Hasta Longinus or Lancea Longinus).
The spear first shows up in episode 12, where the three Eva units need to intercept the Angel by hand before it crashes itself into headquarters. If you remember, Gendou and Fuyutsuki are away in Antarctica (where an Angel blew up, causing the Second Impact) doing "something." On their ship is a mysterious object, long and thin, which takes up the full length of the deck.
This object is first identified at the end of episode 14, which is the recap episode and where Rei and Shinji do the mutual compatability test. Fuyutsuki asks Gendou about the status of the "Lancea Longinus" project, to which Gendou replies, "Going along the plan. The operation is carried out by Rei." The scene then cuts to Unit-00 walking down a corridor, carrying a spear- or lance-like object with the same shape as the one seen in episode 12. Perhaps most interestingly of all, in episode 15 when Kaji shows Adam to Misato, the Spear of Longinus is embedded in the Angel's chest.
This brings up some interesting questions. If the spear was so recently retrieved from Antarctica, how did it get planted into Adam's body? In case you didn't catch on, Adam is the name of the first Angel, Lillith is the second Angel, and the Angel that Shinji encounters in episode 1 is the third Angel. What is the operation that Rei carried out in episode 14? In episode 8, where Asuka and Kaji are first introduced, Kaji is carrying "Adam" in a small briefcase. Did they "grow" Adam, or is the one that Kaji showed to Misato different?
"Eva is made of the same body as mine because I am also one born from Adam."