In a futuristic world, the virtual world is merely a layer on top of reality; within it, cyberpets are abundant and information is plentiful, and it is only visible by wearing special cyberglasses. In Daikoku City, this cyberspace is behaving strangely: cyberpets are going missing, dark entities known as "the Illegal" roam obsolete space that shouldn’t exist, and a large pink antivirus program known as Satchii wanders the streets, attacking both virus and pets alike. Sixth grader Yuko Okonogi has just moved to Daikoku City, and after cyberdetective children help her rescue her lost dog, she soon joins the others in a search for the truth behind these strange occurances.
Shirase Akira is a genius hacker who has earned the nickname "Battle Programmer Shirase" (or BPS for short) for his incredible talent. From saving corporations to global security, BPS is always willing to help a hand -- for the right price. But for skills like his, money is not an option, so be sure to have specialized computer parts, sold-out tickets, or huggable life-sized cat girl posters to spare! With BPS in charge, no computer is safe! That is, if he can manage to stop being a complete slacker...
The reason for this recommendation should be obvious. Battle Programmer Shirase features (amongst other things) 'battle hacking', likewise for Denno Coil. The 'battle hacking' is much more elaborate in Denno Coil than it is in Shirase as there are also more and longer episodes.
One afternoon on her way home from school, Haru saves a cat from getting run over by a truck and promptly gets the shock of her life when it stands on its hind legs to thank her. That night, she is greeted by a parade of felines who inform Haru that her earlier heroics saved the prince of the Cat Kingdom. Haru suddenly finds herself inundated with gifts of mice and catnip as means of thanks, culminating in the announcement that she will be taken to their kingdom to marry the prince. With no desire to marry Prince Lune, Haru turns to The Baron and Muta from the Cat Bureau for help, but unable to stop them, Haru is swept away by a horde of cats. Can Haru prevent this marriage of inconvenience and return home before she becomes a cat herself?
In Yuko and Haru, the viewer will find two very similar protagonists who are portrayed as quite innocent players in the events that are about to unfold. They both show affection for the cuteness of the other characters around them, and are both presented with the task of saving some slightly mysterious creatures. To do this, both Haru and Yuko will have to travel into another reality where the rules are not the same as here.
At first these two young girls look quite lost and alienated from everyday life, following clues and trails that they initially can not even begin to understand. But as the stories progress, the girls will both meet many strange creatures and make plenty of friends, and possibly a few enemies too.
Rumors have it that a monster has appeared over the city, and Yuki would love to catch a glimpse! However, she soon discovers something even more fascinating: a boy named Tetsu not only knows of the monsters, he has a monster pet of his own named Cenco! Yuki is delighted to meet such a creature and tags along with Tetsu to find out more, but soon the two find themselves in the middle of a dangerous conflict with another monster that threatens them and bystanders alike!
Many centuries into the future, humans live as part of the Fractale system, a computer program that moderates their activity to ensure a free and peaceful existence. But while life is indeed comfortable, the cost of growing up in virtual reality communities filled with holographic people called 'doppels' means that it can also get lonely. For Clain living estranged from his parents, adventure finally knocks when he rescues a mysterious girl called Phryne, who appears to be on the run. She spends only a short time with him before hurriedly moving on but leaves behind an unexpected gift: the curious and frustratingly whimsical doppel called Nessa! As Clain learns to adjust to his new friend and survive the scrapes she gets him into, he discovers that she and Phryne are at the heart of a great conspiracy. If he is ever to gain a sense of purpose, Clain will have to leave his comfortable existence and challenge the only thing he has ever known, the Fractale system itself.
Both Denno Coil and Fractale deal with Augmented Reality - even down to the use of "glasses" for viewing the AR. They also both deal with mysterious problems that have sprouted up in the AR world. The AR in Fractale is much further along and more totally essential to the characters' world, but both series do some cool things with the concept.
Furthermore, both anime deal with children finding their own way in the world, and growing up in the process.
Once upon a time, two brothers passed the happy days of their childhood by studying alchemy, which is governed by the equal transfer principle: an eye for an eye -- you can't get more than you give. But these brothers tried to defy that law, and a horrific accident resulted. Now, the older brother, Edward, is called the Full Metal Alchemist because of his metal limbs, and the younger, Alphonse, is a soul without a body, trapped within the confines of an automaton. Together they search for the power to restore themselves, to find the lives they lost so long ago...
I think these two series gives off a lot of the same vibes. Both have strong themes of searching for something from the past; characters that are bad, but at the same time good; and deeper philosophical meanings of what the definition of "life" really is.