Recommend Anime

Bacanno! is very good. So is Monster. Some of my favourites.
My absolute favourite anime is Revolutionary Girl Utena.

Shiki
You can thank me later. If you liked Death note, I can almost guarantee you'll like Shiki. Starts a bit slow, but it's very good. And yes, it's finished. Not terribly long either

I've stopped watching anime regularly, and am really just following the mangas of the ones i like, Ongoing:
HunterXHunter (very weird, but also quite good)
Bleach (THIS SHIT HAS TO END AND I WILL SEE IT)
Naruto (actually getting good again at the end)
History's Strongest Disciple Kenichi (could use a little less fanservice, but whatever)
Hajime no Ippo (fuck yea)
One Piece
Gantz (I have no idea where the fuck the story is going on this, but I like it)
Detective Conan (because mysteries are cool)
Ao No Exorcist (this thing is slow as HELL, but pretty good)
EDIT The Breaker (can't believe i forgot this one. Technically it's a korean Manwah, but it reads the same as a Manga, and is currently #1 on my favorites list)

And I've finished a bunch that I don't feel like listing

Vandread!!! see it love it. (ended)

oh and Hellsing Ultimate OVA (still going but takes for ever.

boku no pico

Bleach, Naruto, Fairy Tail, One Piece, Hunter X Hunter, Death Note This animes very shit^^ DN not bad but not the best.

Code Geass (If you liked Death note you'll probably also like this one. Mecha.)
Stein's Gate (Time travelling meets Microwave. Sci-fi I guess.)
Durarara (Supernatural theme , lots of characters , all well developed.Couldn't stop watching after I started it.)
Darker than Black (Action, supernatural? Animation and plot was good if I recall right,some things were off but don't want to spoil it.)
Kanon , Air , Clannad (Slice of life, Dramas. I personally loved all three but I am a fan of the kind.Also if you plan to watch you should have tissues nearby...)
Lucky star (Slice of life , comedy. Hilarious and laid back.A must watch of the kind.)
Sayonara Zetsubou Sensei (Parody mostly. Tales of a pessimistic,suicidal teacher and his students.)
Arakawa Under the bridge (Comedy. Girl who claims to be a Venusian and lives under a bridge saves a guy who lives by never being in debt to anyone. Lots of strange/amusing characters living under that bridge as well. Quite an interesting watch.)

These off the top of my head.I had some shoujo in mind to recommend as well,but checking what you are watching/have watched does not seem like you'll be into them , at least not yet :). If you specify some genre or need more info on some ask away.Might post again if I have some time later.

Full metal alchemist and Brotherhood

Katekyo hitman reborn.

Eureka seven.

Wolf's rain.

High school of the dead.

Fate/Stay night.

Shaman king.

Yu-gi-oh (but the old one).

TSUBASA: Reservoir Chronicles (the best)

Angel Beats
Trigun
Full Metal Alchemist: Brotherhood (and only Brotherhood)
Darker Than Black
FLCL
Neon Genesis Evangelion
Spice and Wolf
Fruits Basket

Bible Black

Hajime no ippo,Persona 4 the animation,Skip beat,Black rock shooter,Bakuman,Thunder Cats 2011

Hmm, based on what you've seen I would recommend

Gintama

Great Teacher Onizuka

Cromartie High School

Code Geass

Mostly Shounen but they all have similarities with some of the shows you've seen and you might find yourself enjoying some of them.

Fullmetal Alchemist Shintetsu

Evangelion

Berserker

/thread

Code Geass,
Serial Experiment Lain,
When They Cry Higurashi,
Boogiepop Phantom,
Durarara!!,
Baccano,
11eyes,
Infinite Stratos,
Shakugan no Shana ,
Eden of the East,
Blood+

They are all finished besides Shakugan no Shana, that has 2 weeks left until completion.

Evangelion (Old ones are finished. They are remade into 3~4 episodes anime movie with a lot of changes, first 2 have come out)

The Garden of Sinners (7 episodes anime movie. Finished)

Canaan (Finished)

Want to say Fate/Stay Night, but then have to admit the anime is not well made.

I'm old enough to actually remember when these came out, so i have to reccommend a few of them as i havent seen them mentioned.

Akira

Neon Genesis: Evangelion

Cowboy Bebop

Ghost in the Shell

Maocross Plus

These animes aren't simply blast your face off with speed lines and action scenes. These animes have inner meanings and actually tell a story that more likely than not couldn't have been told with live action when they came out (most of these started in the late 80's or early 90's)

Anyway, if you can tolerate a more thought provoking style, these are the best in the business, bar none.

If you haven't watched Cowboy Bebop, you are doing nothing good for yourself.

I also recommend FLCL, Fullmetal Alchemist and Brotherhood, Ghost in the Shell: Stand Alone Complex and 2nd Gig, Rurouni Kenshin, The Big O, Samurai Champloo, Code Geass: Lelouch of the Rebellion, and Hellsing. Also, I too, recommend Death Note for anyone who hasn't seen it already.
Also, just for fun, Lupin III: (Part II at least, not sure how the rest of is...).

Upgrade from naruto,naruto shippuden

Gurren Lagann!
Infinite Stratos!
Gundam series..

Bakuman, Usagi Drop, Stein's Gate (Finished)

Bakuman 2, Another, Sket Dance(Ongoing)

These are some anime which i can think off the top of my head which i recommend. I prefer the slice of life genre and mystery anime in general so my opinion may be biased

Death Note & High School Of The Dead! zee best.

very good + funny = Sunabouzu, Hajime no Ippo, Great Teacher Onizuka, One Outs, Detroit Metal City, Eyeshield 21, Golden Boy.

elfen lied
fullmetal alchemist
fullmetal alchemist brotherhood
hellsing ultimate (ova)

Miria Nikki, Code Geass, Black Butler, Katekyo Hitman Reborn, Full Metal Alchemist, D. Gray man, Deadman Wonderland, Bleach, Soul Eater, Fairy Tail, Ao no exorcist. I highly suggest the first three great animes only Mirai Nikki is still going

Full metal alchemist, Code Geass, Darker than black, D Gray man Elfen lied just to name a few