Gargantia on the Verdurous Planet
Gargantia is one of those wonderful series you do not expect to be so great, even after that dumb term for an explosive in the first episode space battle. Some call him the Uro-butcher, but I call him Ally-Killer Urobuchi in hopes that someone will get the reference.
A show about a boy on a journey in a future run using internet connectivity. Basically, it is "dystopian science fiction Facebook religion the anime". Definitely has come cliche components, but a very solidly made series worthy of respect.
A show about a boy and his super toy who together fight an alien invasion to save the world. This is the only series I have listed thus far which is not dubbed in English, which is an absolute travesty. With appearances from the late Stan Lee, taking place in the USA, and featuring a kid whose both names start with "J", it is more 'Murican than most anime.
Paranoia Agent was an absolute delight of an insane psychological crime story told through many smaller stories following the police in an attempt to find a boy in gold roller blades who attacks people with a golden baseball bat. It goes some amazing places, and truly is a masterpiece. I miss Satoshi Kon stuff like this.
A story of a guy piloting an ancient golem called a "dolom" to save the world from ancient interdimensional aliens from a parallel universe. Remember when Bones imitated Miyazaki and made Xam'd? This is Bones imitating Evangelion and not failing. Dreary tone, incomprehensible plot, and watching the movie afterwards is somewhat necessary to understand how the world works, but that somehow makes it a dang good series.