In the English Dub, when Asuka first meets Rei, she calls her behavior Freakazoid!.
Too many to various world religions (particularly Judaism and Christianity) to list, or possibly even detect.
For a start, all the Angels are named after Angels from Jewish, Christian and Islamic theology and incorporate subtle parallels with their counterparts' names and functions.
Misato initially drinks "Yebisu" beer, a real brand that is depicted correctly down to the label, followed by "Yebichu" beer, a parody of the real label which references the manga Oruchuban Ebichu, of which both Anno and seiyuu Kotono Mitsuishi were fans. Anno later developed it into an anime at Mitsuishi's recommendation.
The Human Instrumentality Project was named after Cordwainer Smith's Instrumentality of Mankind, though they are not otherwise related.
In turn, the Hedgehog's Dilemma is an allusion to Schopenhauer. It's also been theorized among fans that the original ending alludes to and borrows from some of the existentialists, such as Sartre and Kierkegaard.
Toji and Kensuke are allusions to characters from Ryu Murakami's Ai to Gensou no Fascism (The Fascism of Love and Fantasy), from which Anno borrowed much of the psychological material.
Keel Lorenz is an allusion to the ethologist Konrad Lorenz. He was originally named Konrad, too.
Konrad Lorenz developed the concept of imprinting in terms of mother/child relationships. For example, say you've got a duck's egg in an incubator, and it's ready to hatch. The eggshell cracks, and the chick's head pops out. It sees you, and thinks, "Mother!"
Interestingly, this series is the one most referenced by later Gainax works, and possibly anime in general. Yes, even Gurren Lagann, although it can be looked at as a Take That at NGE overall.
The manga seems to have shout outs to Star Wars, of all things. For example, on a NERV writeup of Toji, there's a documentation of his Midichlorian count. In a recent chapter, Gendo also pulls a Darth Vader on Shinji, which is reminiscent of the fact he loses a hand in The End.
Misato mutters "I have a bad feeling about this" in the episode with Jet Alone.
The title of the latter half of The End of Evangelion, "Magokoro wo, Kimi ni," comes from the Japanese title of the movie Charly, which was based on the short story/novel Flowers for Algernon.
Devilman and the Ultra Series get multiple shout outs throughout the series, some subtle, others overt.
According to Anno the Devilman ones were unintentional and he only noticed the similarities when they where pointed out to him. Interestingly, one of the two unused, proposed endings to Episode 26/End of Evangelion was even closer to Devilman's ending than the final version.
A blink-and-you'll-miss-it one comes in form of one of Shinji's t-shirts, which has the logo of the British New Wave Music band XTC on the back. Seeing as quite a few of XTC's songs revolves around some of the same themes as Evangelion, the reference is likely more than just a superficially one.
The scene where the military attacks NERV HQ is an homage to Hideaki Anno's favorite film, Battle Of Okinawa, right down to the use of flamethrowers.