Well then.
This is my kind of thread.
First, this:
Take that with a grain of salt as there are some missing.
As for my personal recommendations, There is:
Neon Genesis Evangelion
An angsty sci-fi set in the near future featuring giant bio-mechanical war machines punching things.
Gurren Lagann
An incredibly over the top action-sci-fi featuring big robots punching things, bigger robots punchings and robots the size of galaxies punching things.
Kaichou wa Miad Sama!
A romance/drama slice of life detailing the relationship between a girl who hates boys and a boy who is infamous for rejecting girls advances.
Each of these are my personal favorites.
EDIT:
Almost forgot:
5 Centimeters Per Second
What can I say about this.
It is one of the most bittersweet romance movies I've ever seen.
I cry every time I watch it, and I love it.