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Essential doesn't mean best or favorite. Here's a list based off influence or cultural significance:
Evangelion obviously.
Bebop for Americans, or some other whatever was one of the first anime series to make it big in your country.
A Miyazaki film.
Mobile Suit Gundam, seeing as how pervasive mecha has become in anime.
K-On!, Haruhi, or Lucky Star. You can't deny their influence whether you like them or not.