What Are Some Of The Best Japanese Anime And Why?

The order mentioned below doesn't really mean anything in terms of quality of the story or whatever. I'm just writing down stuff as I remember them.
1) Call me cliched, but,
Fullmetal Alchemist
Just the story is enough to give any person, with even the smallest trace of humanity, goosebumps
This part really killed me.
(If you're wondering what that means, google it. I won't spoil it for the people who haven't watched it yet.)
Brilliant story. Regardless of whether you choose to watch Brotherhood( Which sticks to the manga) or the old anime, you will love it. Perfectly portrays the bond shared by a boy and his younger brother, and their interactions with different kinds of people. Some good, others bad. But, something that sticks with you is that each one of them has a story to tell. The way the atrocities of war have been portrayed is heart-wrenching. Personally I think a good reason I loved the story was because of the soundtrack( Which is the case with 70% of all the decent anime out there), kinda gets you into the mood, if you know what I mean.
All in all, kickass.
2)
Fate Zero or Stay/Night(referred to as SN)
Conceived by Type-Moon (which happens to create a lot of awesome visual novels namely, Shingetsutan Tsukihime, Kara No Kyokai (or Kyoukai, Japanese names all sound the same to me)
I've asked a lot of people what they felt about these two (I love discussing anime,
make sure you don't bring up anything that's anime-related, or I just might talk you to death.) and what I found was that people liked Zero over Stay/Night.
Personally, I liked both. Why?
7 Heroes. 7 Masters (read mages or sorcerers.). 1 Holy Grail (Yes, THE Holy Grail.)
Battle To The Death. How awesome is that? Apart from giving you a lesson in history, these two take you on an awesome journey into age old wisdom and values. Valor, courage, integrity. Call me an idealist, but stuff like this just makes me feel :3. I did notice that Zero makes a much better endeavor at all of this than SN. But, I saw SN when I had just started watching anime ( around 7 years ago) and I guess nostalgia's clouding my judgement.
Really good anime and worthwhile your time. (Though I just couldn't get myself to play those visual novels. Click,click,click,read,click,save,click... Arrrrgghhh)
3) Aoi Bungaku
It's not really a properly laid out anime series, but, rather a rendition of popular books in Japanese culture into anime.
12 episodes, with 3-4 episodes devoted to a single story. Some of them sucked, but I personally liked 'Ningen Shikkaku' and 'Hashire, Melos' One pretty dark and disturbing, the other pretty sentimental. Awesome.
4) Tengen Toppa Gurren Lagann
I have just one word for this;EPIC! FANTABULOUS! HOLY CRAP! ... Okay, maybe not 'one' word. But, you get the point, right?
I don't really like mecha anime, and I was going to forego this. I thank the stars that day for introducing me to this unbelievable piece of art. This is INSANE!. A story about the indomitable power of the human spirit. Giant robot enemies? No problem. Giant space-ship like aliens? No problem. Giant Asteroid sized aliens? No problem. GIANT FREAKING, HUMONGOUS, GALAXY SIZED SUPER MECHATRONIC BALABOLLOCKS?( I have no idea what that means, but what I mean is something really, really big) No problem. That's how big this anime is.
( Yes, that's space, those are galaxies, and that is a friggin' giant robot)
Determination, badassery, grit and all the good stuff. Definitely a must watch,
5) Clannad
Okay, I'm pretty sure you must've wikied the title already and apart from some Irish band you got the link to a visual novel. Don't judge the anime before you watch it. Now unless you're some really badass, don't-give-a-damn, heartless person with emotions the size of a sperm's tail ( pretty small is what I mean to say), there is no way in the world you aren't going to cry in this series. ( Unless you get bored after season 1. The good stuff's in After Story. Then again, Code Geass got interesting in season 2 as well, so if you got through that, you can get through this too.) I watch one particular episode and I get a free ride on an emotional roller coaster The whole world's nice, everyone's friendly, no wars ( No, I'm not high, its just Clannad). Good stuff.
I can't really remember more, because my brain chip just got fried. I'll put some more up as and when I remember them. Till then, knock yourself out with these. Better than anything you've ever seen, heard or tasted. Cheers!
Edit: Some more food..
6) Psycho Pass
When I first heard about Psycho-Pass, I thought it would be something like Ghost In The Shell (Pretty decent. Worth a shot). Was I wrong. GITS does its best to confound you and give you a serious migraine. Psycho-Pass, on the other hand, is a seamless thriller set in a utopian futuristic society where your mental state is determined by your body language, the pheromones you secrete and blah blah blah. If the cameras so much as sense that you're having a bad day, you're immediately sent to a correction facility to stop you from turning into some latent criminal. What's important is the fact that there's no judiciary. Yes, no judiciary. And how do these guys live peacefully, you ask?
Introducing: The Sibyl System. A secret A.I. system (Much like Skynet) that sets benchmarks on what qualifies as anti-social behavior and what doesn't. SO what it means is........ you so much as swear at the guy who puts an extra lump of sugar in your coffee and you get hauled off to some criminal rehabilitation center thereby screwing your entire life. GG
But, the story isn't about the system. Yes, with all the other anime, we have a cute lady detective( ^_^) who's sent on some gruesome cases and in the end, begins to doubt her purpose and the system's purpose. THIS IS A MUST WATCH.
7) Apart from the above, ( because I'm really getting too tired writing down everything, I'll just leave the rest to you) I seriously suggest the following anime:
Shigurui
Steinz; Gate
Usagi Drop
Rurouni Kenshin ( Should've mentioned this one earlier. The OVA's are exceptionally brilliant. I can't see too many directors making an impact like that.)
Neon Genesis Evangelion *yawn*( Still deserves a mention, though.)
Emma- A Victorian Romance ( Yes. I do like a bit of romance now and then.)
Nana ( Again)
Hanasaku Iroha
AnoHana ( This one went totally Clannad on me.)
Honey & Clover
Serial Experiments Lain ( Weird)
Ergo Proxy ( Weirder)
If you don't have the patience to watch whole series, you could just watch the following movies
OVAs: Rurouni Kenshin
End of Evangelion /Remake of Evangelion
The Girl Who Leapt Through Time
5 Centimeters Per Second ( :') )
Ghost In The Shell: 1, Innocence, Solid State Society ( This one has an amazing story! Mother of all hypothetical conspiracies!)
Also, there's something called Genius Party ( Really don't know what to call this) It's a series of single episode shorts made by upcoming artists.
Bake-, Nise-, Neko- monogataris
Spice & Wolf.