My first introduction to anime was with Fullmetal Alchemist: Brotherhood, and I absolutely loved it and have continued watching various animes ever since. While I wouldn't quite call myself an anime junkie--there are a lot of popular shows I still haven't watched, and I still watch lots of non-anime stuff--I do have a deep appreciation for quality anime in the same vein as FMA:B. Here are a few of my favourites on Netflix that I would highly recommend to anyone who has a liking for anime.
1. Black Butler
Black Butler is my all time favourite anime series. Black Butler was just recently taken off of Netflix, much to my dismay, but it's too good for me to not put on here. I first discovered this series a few years ago, and have watched it at least three times through. Ciel Phantomhive is a complex and unexpected character, both in his ruthlessness and his humanity as he navigates the cruel and cutthroat criminal world as the Queen's watchdog. It is no wonder that his demonic butler, Sebastian, is so perplexed with Ciel, how he lives in the mire of darkness but his soul remains pure and true. Black Butler is fantastic--it's dark, funny, and thoughtful, with both riveting characters and story lines, and is overall an excellent calibre of anime. You are drawn into the story, and develop real affection for the characters. It's the first thing I recommend to anyone looking for quality anime (QED it's first in this list--I believe it's on Hulu and some slightly shady websites), and I plan on re-watching it myself many times over.
*Caveat: There are now two seasons of Black Butler, the original series and a kind of extra series that extends from season one but focuses on a different pair of characters. I strongly, strongly recommend that you do not watch the second season. It is messy, the characters are annoying, and it ruins the otherwise ambiguous but good ending of the original series.
2. Blue Exorcist
I think that Blue Exorcist has one of the arguably most bizarre premises for any anime I've watched: the human son of Satan trains to become an exorcist to get revenge on his father. I don't blame you if you're sceptical--I certainly was when I first gave this show a try. But I am so glad that I did finally get around to this show because it is fantastic. It nicely balances humour, intelligence, and the dark subject matter--I would give it a close second to Black Butler (QED this is #2). I think one of my favourite stylistic aspects is that it plays off of many of the high school anime tropes, but with the setting of a life-or-death struggle with the powers of the demon realm. Blue Exorcist also does an excellent job grappling with some complicated ideas, like the corruption of high (and supposedly holy) power, the loss of loved ones, and how blood/family does not determine what someone has to be. I devoured the first season of 25 episodes in only a couple days, and I can't wait to see season two, which is slated for later this year.
3. The Seven Deadly Sins
Seven Deadly Sins is an original Netflix series, done through Aniplex. You might be tempted to think of the sins/homunculi from FMA(B), but that's not what this show is about. It starts off pretty innocently--a boy tavern keeper and a runaway princess--but the plot doesn't take long to thicken, with Holy Knights, magical powers, and a plot to overthrow the kingdom thrown in for good measure. The Seven Deadly Sins--seven exceptionally powerful Holey Knights--must fight to restore balance and justice in a kingdom that is about to topple into the hands of a corrupt, demon-powered few. The catch is that the entire kingdom believes the Seven Deadly Sins betrayed the kingdom in a massacre of Holy Knights that happened ten years ago. This show may not be all that deep and philosophical, but the story line and the story telling are as good as any other top quality anime. It's a good, entertaining show for a lazy weekend.
4. K
I took a chance and decided to watch K--I'd never heard anything about it, and I still haven't, but I found it to be quite good and intriguing. The premise is different and takes some getting used to. There are seven ordered kings, each with their own power and dominion, and each king leads his clan. This show is mostly about the third and fourth clans--the Blue King and the Red King--fighting each other to see who can catch an alleged murderer, Yashiro. There also happens to be a pretty awesome samurai butler type man who gets to Yashiro first. Unfortunately for everyone, Yashiro just seems to be a normal high school student, insisting on his innocence. This show is clever and unexpected in many ways (though, the Blue King does remind me an awful lot of Roy Mustang from FMA(B)). It stands apart from other shows because of, for lack of a better word, the aesthetic of the art style and its ambient music. Most of the art seems washed out, with lots of blues and greens, and the music takes up any non-talking space. It's strange and different, but you get used to it after a few episodes. The show is a short and sweet 13 episodes in all, encompassing an entire and satisfactory story that is well-paced and interesting.
If you're already familiar with the anime world, you'll notice that I did not include Death Note on this list. Frankly, Death Note bored and irritated me a great deal. The first third or so was interesting enough, but then the show just dragged...and dragged...and dragged... Despite its acclaim, I can confidently say that Death Note is not worth the 37 episodes it takes up, and should be skipped in favour of shorter, better series.
So, there you have it, my four favourite anime shows to date. All of them are on Netflix, sans Black Butler. Go forth and watch some good anime!