Sora yori mo Tooi Basho - Absolutely wonderful. Starts as your standard cute girls doing cute things but it's incredibly well done and likely to make you break a tear now and then. About a few girls who decide they want to go to Antarctica (I know, it sounds dumb... try it ayway!)
Shoujo Shuumatsu Ryoukou - Another CGDCT anime, though relatively slow paced the way the characters are done absolutely makes up for it. About 2 girls surviving together in a post apocalyptic world.
(man this thread seems old...)
Boku no Hero Academia - Absolutely must watch this if you like Shounen, one of the best anime's to have come out in recent time. Great characters. About a world where people grow up having superhuman abilities and the hero culture that rose up with it.
No Game No Life Zero (Movie) - Damn. I think even if you don't like the series (No Game No Life) because of the ecchi comedy in that one you may still like this movie. It still retains a little of that but has a way, way more serious tone. Moving and touching. You'll probably get more out of it if you've watching the series but even without I'd say it's well worth watching.