Neon Genesis Evangelion is set after the world has been decimated
by something called the "Second Impact".  The world has rebuilt and it's
14 years after the event, and the threat of the Angels (who were somehow
responsible for the Second Impact) and were set upon destroying mankind.
However, humanity is ready and had developed specialized mechs called
EVA's which used stolen Angel technology.  The only people who could
pilot these mechs were 14-year-olds, specifically ones who were conceived
during the Second Impact.  
    The main character is named Shinji Ikari.  His father was the 
one whohad developed the EVA units, but they have a particularly 
distant relationship and that tension shows up whenever they speak to 
each other.  He pilots Unit-01.  He is taken care of by Katsuragi
Misato, one of the majors in charge of the project.  She is intelligent
and resourceful.  She's had quite a bad past, which is explained in the
story.  The other EVA pilots are Rei Ayanami and Asuka Langley.  They pilot Unit-00 and
Unit-02, respectively.  Rei is almost like a robot, showing almost no
emotion.  In fact, she only shows emotion when Gendou, Shinji's father
is involved.  The fact that she is closer to Shinji's father than he is
is an important issue in the story.  Asuka is outspoken and has the 
highest sync rate for the EVA's out of all three pilots.  She wants to
literally outperform everyone in all of her actions.  She's had some
terrible things happen to her as well, which might explain why she acts
that way.
    This is a very close second fo Escaflowne as my favorite anime.  
It just might have a stronger storyline than Escaflowne.  This is another
anime with mechs where not a lot of the focus is centered around the
mechs, but on the people who pilot them.  The human quality of this 
anime surpasses even many big budget movies.  It allows you to understand
what motivates each character in doing what he or she does.  I love 
the way each character must put their own emotions aside to battle for
the fate of mankind.  Definitely must watch it.