Some favorites that I've read:

Azumanga Daioh
GinTama
Claymore
Gantz
Kurosagi Corpse Delivery Service
Kashimashi
Bakuman
Death Note
Chobits
Liar Game
We Were There
Beauty Pop
Kitchen Princess
GTO
Sunshine Sketch
Dragonball
Genshiken
Toriko

naruto manga
one piece manga
bleach manga
Fairy Tail
The World God Only Knows
Beelzebub
Air Gear
……
……
……
blablabla...

vampire knight
Backstage Prince
Hana Kimi
fushigi yugi
fushigi yugi genbu kaiden
Black Cat
Bleach
Cardcaptor Sakura
Clannad
Code Geass: LeLouch Of The Rebellion.
D.Gray-Man
Death Note
Fate/Stay Night
Fruit Basket
Inuyasha
Ouran High School Host Club
Gakuen Alice
Rosario+Vampire
Tokyo Mew Mew
absolute boyfriend
xxxholic
bloody kiss
D.N.Angel
millenium snow
wanted
pixie pop
godchild
black bird
the magic touch
st dragon girl
chibi vampire
nabari no ou
pichi pichi pitch
ai ore
black god
maria holic
inukami
omamori himari
puchi hound
her majesty' dog
the betrayal knows my name
kaine
blood hound
camelot garden
the devil within
wolf's rain
the night of the beast
fall in love like a comic
the king's pawnshop
gokko
the tail of the moon
love phobia
and a lot more...

Blue:exorcist
psyren
code breaker
defense devil
beelzebub
Corpse Party Musume
Blood Lad
ubel blatt
Watashi ni xx Shinasai!
Unbreakable Machine Doll
medaka box
Unbalance X Unbalance
witch hunter
and many more

so many...
naruto
bleach
beelzebub
one piece
hunter x hunter
kaichou wa maid sama
clannad
beauty pop
kimi ni todoke
kimi iru machi
sailor moon
fairy tail
katekyo hitman reborn
soul eater
natsume yuujinchou
xxxholic
mushishi
noblesse
bakuman
toriko
dragon ball
air gear
bleach manga
fairy tail
one piece manga
beelezebub
the world god only knows
so many

one piece
naruto
bleach
Boku no Hatsukoi wo Kimi ni Sasagu
Charisma Doll
Fall in love like a comic
Power
Gokusen
Koukou Debut
Kaichou wa Maid-sama
Meru Puri
there are many
just read bleach 495

Gamaran
Defense Demon
Code Breaker
Kurogane (Kezane Haruto)
and Karate Shoukoushi Kohinata Minoru

-Bakuman
-Genshiken
-Otoyomegatari
-Usagi Drop
-Vinland Saga
-Moyashimon
-Nausicaa
-Cross game
-Gunnm
-Black Lagoon
-Nurarihyon no Mago
-Shingeki no Kyojin
-Yotsuba&!

These are the series I have either completed or read every available volume. I have read many others without completing them.

Thanks to Allmangasreader . com I can have a whole list of all the mangas I've read
Some of this are still ongoing, so I read them when they are released

Akira
Ao Haru Ride
Ashita no Joe
Battle Angel Alita
Beck
Buyuden
Corpse Party Blood Covered
Deadman Wonderland
D.Gray-Man
Dragon Who
Gangsta
GetBackers
Gintama
Good Ending
Haikyu!!
Hell's Kitchen
Hi no Tori
Ichigo 100%
Katekyo Hitman Reborn!
Level E
Liar Game
Love Hina
Love Junkies
Mysterious Girlfriend X
Nurarihyon No Mago
Rurouni Kenshin
Sensei no Bulge
Seto no Hanayome
Sket Dance
ST&RS
Vagabond
WANTED
What a Wonderful World!
Yamada-kun to 7-nin no Majo
Ao No Exorcist
Bakuman
Beelzebub
Bleach
Boku wa Beatles
Btooom!
CROSS )
Dragon Ball Multiverse
Enigma
Fairy Tail
Gamaran
Hungry Joker
I'll Give It My All... Tomorrow
Inumarudashi
Kagami no Kuni no Harisugawa
Kurogane
Magico
Naruto
Nisekoi
One Piece
Romance Dawn
School Rumble
Shaman King Flowers
Silver Spoon
-SINS-
Slam Dunk
Terror
The Devil King Is Bored
Yamada and the Seven Witches
Yankee-kun to Megane-chan MangaYankee-kun to

One Piece
Naruto
Bleach
Death Note
Skip Beat!
Vampire Knight
Prince of Tennis
Fairy Tail
Bakuman
Code Geass: Lelouch of the Rebellion

The only manga I ever read from beginning to end is Elfen Lied.

I also read Bleach but it's only from the part that the anime stopped on Ichigo and Ulquiorra's final fight to Ichigo losing his powers and how's he trying to get them back and Naruto but it's only one volume that I brought that have Sasuke trying to get Juugo on his team to fighting Deidara.

Naruto
Bleach
One Piece
The World God Only Knows
Medaka Box
Kimi no Iru Machi
Suzuka
Sora no Otoshimono
The Melancholy of Haruhi Suzumiya
Kore wa Zombie Desu Ka?
High School of the Dead

a lot!!
prince or tennis/new prince of tennis
gakuen alice
hiyokoi
another
oresama teacher
super lovers
cinderella collection
arisa
shounen butterfly
ato no matsuri
lovely everywhere
binmougami ga
accel world
reversible
alyosha
fun fun factory
glamorous lips
air gear
zombie loan
pandora hearts
d grey man
naruto
ao no exorcist
ao haru ride
flat
mairunovich
love stage
nowhere boy
tonari no kaibutsu
tamago no kimi
kimi no todoke
last game
only you dont know
bonnouji
yankee-kun to megane-chan
two colours
chronos-deep
film girl
hitsugime no chaika
one piece
hunter x hunter
fairy tail
skip beat
bakuman
beelzebub
toriko
tenkyuugi - sephirahnatus
ikoku meiro no croisee
eternal moment
ouji to hero
high school of the dead
akuma to love song
dogs: bullets and carnage
+C sword and cornett
youko x boku
ookami heika no hanayome
rec - kimi ga naita hi
fairial garden

there are a lot more but im getting lazy soo..... these are the manga that i especially liked! i read anything as long as they have a nice start and art!

oh, man
there are many
one piece
bleach
naruto
slam dunk
i''s
kaiji
kimi....
Deathnote
Zettai Kareshi
Kare Kano
Perfect Girl Evolution
Gakuen Alice
Ouran Hig
.
.
.
.
.
.too many
and i am just reading fairy tail 287

I actually haven't read a whole lot of manga. Recently, I've been reading; "Tarot Cafe", "Totally Captivated"<-really enjoying this one , I've started "Peach Girl", and "Vampire's Portrait".