You have some good tastes, my friend. :)

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I'm gonna cheat a little. I don't like to mix the current anime I'm following with shows I've watched in the past, since I find it creates bias. For example, I loved stuff like DBZ and Digimon when I was a kid, but I find I really can't enjoy them nowadays. Same with Naruto...though that was actually a lot more recent; and mostly to do with how much the later arcs soured my experience.

That being said...it defeats the point of the question if I just list shows that have already finished...so I'm putting down two top 5 lists instead of one top 10. I also read a lot more manga, but since my favorites all have anime adaptations, I'm gonna put them down regardless of how much I've seen of the anime.

Favorite Ongoing

One Piece (only read the manga)
Seven Deadly Sins
Fairy Tail (seen a bit of the anime, but prefer the manga)
Nisekoi
One Punch Man

Favorite Completed/Legacy

Fullmetal Alchemist: Brotherhood
Toradora!
Hunter x Hunter*
Tengen Toppa Gurren Lagann 
Code Geass

*Yeah I know it's not completed, but the anime is. And considering how the author has written like 10 chapters since 2012, I'm considering it a legacy series until the manga picks up again.

1. Fullmetal Alchemist Brotherhood
2. Toradora
3. Parasyte the Maxim
4. Fullmetal Alchemist (original)
5. Psycho Pass
6. Madoka Magica
7. One Punch Man
8. Soul Eater
9. Ouran Highschool Host Club
10. Persona 4: The Animation

Probably will change once I finish some series I'm planning on watching but these are my top 10 as of now

Some favorites off the top of my head, no particular order:
Inuyasha
Fullmetal Alchemist
Cowboy Bebop
Trigun
Girls Bravo (in a way)
Avatar: The Last Airbender (I know it's not of Japanese origins but the style is there, that's good enough for me)
Eyeshield 21
Haruhi Suzumiya/Yuki Nagato spinoff
Bleach
Monster Musume
Abenobashi
FLCL

Currently watching:
Ika Musume
Umaru-Chan
One Punch Man

10) Sailormoon (Yes, it makes me think of the wrong things. lol!)
9) Everything Becomes F: The Perfect Insider
8) JoJo's Bizzare Adventure: Stardust Crusaders
7) Durarara
6) Code Geass: Lelouch of the Rebellion
5) The Irregular at Magic High School
4) Psycho Pass
3) One Punch Man
2) Full Metal Alchemist: Brotherhood
1) Your Lie In April

1. Dragon Ball

2. Cowboy Bebop

3. Outlaw Star

4. Trigun

5. Space Dandy

6. Tenchi

7. Kill La Kill

8. Naruto

9. Attack on Titian

10. Ghost in a shell.

Wow, people seem to watch not many animes here. I have to toss out Grave of the Fireflies so I can even pack my 10/10s in a top 10 list.

These are not in order except for my number one. They're all equally great.

1. Kill La Kill
- K-On
- Azumanga Saioh
- Shirobako
- Junketsu no Maria
- Claymore
- Clannad After Story
- Toradora
- Yuuki Yuuna wa Yuusha de Aru
- Higurashi

Having a top 10 is quite silly though. I could name another 100 animes that are truly great (9/10).

http://myanimelist.net/animelist/vivster?status=2&order=4

Quite a few Mainstream Ones on my list (but who cares, i love them :D)
1. Steins;Gate (Easily my number 1 as i love time travel settings. Especially more dramatic ones)
2. Code Geass
3. Shingeki No Kyojin (I don't care what anyone says about it being overrated, i love the setting and i love the animation. Just such a joy to watch)
4. Shigatsu Wa Kimi No Uso
5. The Garden Of Sinners
6. Death Note
7. Fullmetal Alchemist Brotherhood
8. Rainbow Nisha Rokubou No Shichinin
9. Hunter X Hunter 2011
10. Kuroko No Basket (If the first season wasn't weaker than the other 2, Kuroko would easily be in my top 5)

Honorable Mentions:
- Zankyou No Terror
- The Melancholy Of Haruhi Suzumiya (The Movie is in my top 3)
- Fate/Zero
- Mushishi
- Welcome To The NHK
- Puella Magi Madoka Magica
- Higurashi No Naku Koro Ni
- Ping Pong The Animation
- Great Teacher Onizuka
- Darker Than Black

NIce thread I will have a think about it.

ATM i started watching One Piece as have herd good things, Have seen 153 episodes in 2 weeks lol

1. Dragon Ball Z
2. Naruto
3. Bleach
4. Fairy Tail
5. Rurouni Kenshin
6. Yu Gi Oh! Duel Monsters
7. One Piece
8. Fullmetal Alchemist 2003
9.Hunter x Hunter 2011
10. Death Note

1: Code Geass
2: Bleach
3: Inuyasha
4:Stein's Gate
5:Trigun
6:Baccano!
7:FMA/Brotherhood
8:Yu Yu Hakusho
9:Death Note
10:One Piece

I am sure that my 5-10 changes daily though......

Edit: Yep Rurouni Kenshin is actually somewhere in there, at least the first half of it.