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Yuko from Ef-A Tale Of Melodies fits into this category pretty well. Though her story isn't explained much until the latter half of the series.

Only a couple parts felt slow.
It all seemed like random action, but it is an IC after all.
So, pretty good

Silent Civilian - Divided

On Time!!
Sign me up!

Gary Jules - Mad World

Pokemon Stadium 2 for N64
<3333333

FM Static - Man Watcha Doin?

Shit sucks.

Animatrix - The Second Renaissance Parts I & II, features some pretty graphic robot scenes.

Whitechapel - Devolver

Opeth - Hessian Peel