Amatsuki

They're both about the interaction between 'ayakashi'/'youkai' and humans. 

They are very similar: the age where both of them take place and the fact that both have youkais too. And one more thing: Kantarou and Toki are both connected to a tengu some way. And the style is alike too. 

There's that one boy who until recently has been living a normal life, but is suddenly teleportated into another world. At first everything is messed up, but after awhile he gets used to the new life. The thing is that apparently he is the chosen one to get rid of the evil that's hiding in the shadows. But all is well when it ends well! In both Kyo Kara Maoh! and Amatsuki we see the development of the lead male characters who are destined to bring peace and prosperity to the other world they suddenly appear in. 

Similar styles in line quality, one more light and carefee, the other more Gothic, both rather realistic in character detail, both deal with historical AUs. The stories have quite a bit of depth to them. 

.hack//SIGN is about people getting stuck in an MMORPG video game where as Amatsuki is about people getting stuck in a virtual reality Japaneses history machine and sent to Japan's past. Both have an interesting story but have very close similarity's. Amatsuki is very slow at the start but begins to pickup as characters and plot are introduced. 

both deal with supernatural non human beings and similar style of art 

Both animes have historical elements, yōkai and a similar art style. If you enjoyed one of them, you'll definitely enjoy the other as well. 

Fictional stories relies on a number of themes. Among them is a chance encounter with certain forces of the supernatural. In both series, the main protagonist encounters them in the very beginning that threatens the very existence of their lives. Action wise, both series focuses on fantasy themes with its weapons and execution in terms of its fighting elements. The place that both series takes place are also influenced by its historical setting. Rikugou (Amatsuki) and Jinbei (Mushibugyou) also shares similar personalities in terms of being kinda to their peers as well as protecting what they treasure. Their encounter with a strange female character in the series creates a bond that is noticeable throughout their perspective stories. read more 

The protagonists of both shows are normal students who are suddenly drawn into another world (both literally and metaphorically), due to them possessing a very special power. 

Both have modern and non-modern aspects to the story line. They also have demons of some form or another. The characters help to draw the viewer into the story and the art styles are also very unique. 

In case you were amused by how the definition of Good & Evil got alternated in Amatsuki, you're gonna enjoy Kuroshitsuji as well. 

In both series, a normal boy ends up stuck in another world. MCs face a lot of trouble and have a hard time fitting in. There are magic/mythical creatures. MCs are forced to fight for their lives. 

Set in similar era, has supernatural themes and melancholic feel to it. Both deal with dark mythological creatures and unsolved mysteries. Amatsuki has more fighting, confused main character, time-travel and it is plot-driven. Mushishi depicts different setting every episode and has a master in 'mushi' as a main character.  

High school girl/boy trapped in the past. Samurai. 

similar period time and fantasy, time travel  

same beginning...a common school student is suddenly transported into some alt world that resembles old ours. and there is a prophecy about them there. 

Boy who doesn't listen in history class gets trapped in history. Nobunaga Concerto is more in tune with the actual history of the Sengoku Period whereas Amatsuki is such a gratuitous fantasy Edo such that it might as well be any random fantasy world, despite being based on a real museum (the Edo Tokyo Museum). Nobunaga Concerto has a much more engaging protagonist and bounces off from weird anachronisms, the 3D works oddly well. Amatsuki takes itself more seriously which in turn makes it appear rather silly. Neither are ever going to get a season 2 despite cliffhanger endings. Ha. 

The main character is stuck in a "game" that becomes his new reality. 

Amatsuki is a newer series that places a modern character in the middle of a self-contained land with its own lore, past and rules similar to The Twelve Kingdoms. (Note: Amatsuki is far more comparable to this series than Saiunkoku Monogatari. Saiunkoku is a bishounen heaven with romance and drama surrounding a strong female lead. Twelvel Kingdoms, on the other hand, lacks the romance and lacks focus half the time.) Amatsuki has a male lead in comparison to Twelve Kingdoms and he is far more capable than Youko. By the cover art, you would assume Twelve to have a lot of action involved in it, but it doesn't. It has intermittent action that's mediocre at best and focuses more on politics and introversion in part of the chapter focus lead(they vary). Amatsuki is, as of the only season, better paced with a good deal of coverage in terms of action, story and politics. It also has fantasy elements with more in-your-face magic as well as swordplay, which The Twelve Kingdom lacks. If you liked Twelve Kingdoms, or in particular, if you liked the concept but didn't like the delivery--I suggest you switch on over to Amatsuki. However, be forewarned.. much like Juuni Kokuki, Amatsuki ends abruptly. From what I've read, Amatsuki is based on a long running manga series and only the beginning ever got animated. read more 

Here's the story: "One boy suddenly is dragged into a whole different world and after overcoming great hardships saves that same world" And it's like this not only in Zero no Tsukaima but also in Amatsuki. The lead male character is constantly hesitating whether he does the right thing or not. The thing that's the most interesting is whether Toki will stay like Saito or will leave if he has the opportunity at the end of the series? 

Both of these Anime twist historical with sci fi into it. They also have a horror feel to it, though to a majorly scary one. Both series left me wanting more. 

The supporting characters have quite a bit of character depth. They are also dealing with being able to see spirits, while others do not. The art styles are also very realistic and crisp. 

Both shows feature protagonists who live normal high school lives, but are soon dragged into large, action-packed adventures. 

Both are about boys who go into something that starts off as and illiousion. Then they get stuck in another world. They have freinds who help them in almost everything. The boys both can be smart ( the one in Dragon Drive when he wants to).  

Both have demons in them, in different asspects. Except Yagaya no Oinari-sama is a lot more light hearted then Amatsuki. The quirks are quite familiar. 

This recomendation is made for the Anime viewers who are looking for any Anime that contains "time travel" and "supernatural". The stories leave the viewers wondering what will happen to the characters. 

Both set in the samurai Edo period, with shigurui being more violent and Amatsuki more laid back 

In both the main character is dragged to an unknown world where they have the power to change its destiny (and are unaware of it) 

The stories feature an alternate reality that is reached via means of sci-fi. They go two different routes story line wise, but the main characters have similar personalities. There is also the good fight to be something more then the "loser". 

Comradeship plays an important role with the characters and there is a group that wants to control what the main character does because he has a special power. The art styles are also beautifully crisp and the series has quite a few amazing characters with a lot of depth. 

Historical shows (different eras though) that involve adventure, action, interesting cast, and - to a lesser degree in Brave 10 - supernatural elements. Both shows also give off the same feeling of great potential, but they're not quite there.