Two errand-running orphans who pilot a small airship save a girl and go on an epic adventure to save the world. Absolutely fantastic series. I am surprised that the production studio that made this was able to briefly pull itself from the gutter to make this, as Gonzo has a long history of making garbage and smut. With such titles as Strike Witches to its name, I am amazed that Gonzo made anything this perfect.
Birdy the Might: Decode
Alien supersoldier police lady and the school nerd share a body due to a tragic accident. Personally, I would suggest reading the Bidry the Mighty II manga instead. While the anime is fantastic, it ends without final resolution and goes in a different direction from the manga. Even so, it is absolutely fantastic, and definitely worth your time on its two seasons. Also, there was certain plot elements added and removed from the manga, which are a net loss, but dang is the animation gorgeous.
Xam'd: Lost Memories
An ambiguously fantasy or science fiction series about nature against technology. Imagine what would happen if studio Bones decided to try making a Miyazaki-style project, because that is exactly what this was. Yep, it is like Eureka Seven and Nausica had a baby.
Noein: To Your Other Self
A series about time travel, parallel universes, and regret. This is one of the few anime I have seen with such a shoujo aesthetic that was so fantastic and great. Also, the music in this series is the stuff of legends. I once made the following post about it, because Noein is so unfairly underrated and forgotten among the crowds.
This fantasy show's dub is somewhat dated, but dang is this show dumb fun. World's dumbest wizard on an adventure as he punches his way to victory through dark dungeons and elven forests? Worth giving more than just a chance!