Naruto, Bleach, One Piece (The Big three of Shonen Jump, though I highly recommend One Piece over both Bleach and Naruto to be honest),
Dragonball/DBZ (A must for any manga reader)
Detective Conan (Case Closed, genuinely intriguing series built around mystery and inspired by the work of Arthur Conan Doyle's Sherlock Holmes)
Buso Renkin (A fun short series)
Black Cat (Amazing and awesome)
Berserk (
BLOOD GUTS TITTIES!!!! And one well developed story, it's been in serialization since around 1988)
D.Gray-Man (Really fun to read, based around an alternate end of the 19th Century)
Death Note ('Nuff Said)
Bakuman (By the guys who did Death Note, this is a manga, about manga)
Katekyo Hitman Reborn (Baby Mafia Hitman with magic bullets that make people act out their dying wishes by ripping off nearly all their clothes, hilarious, but also quite action packed)
Soul Eater (Really cool art style and an interesting story)
Fairy Tail (I could say One Piece but with magic instead of pirates, but that'd be lazy and somewhat of a lie, but if you like/love One Piece, you will definitely love this)
Rave Master (By the guy who did Fairy Tail, this is his first work, really fun to read),
Shaman King (Fun series to read about dead spirits who fight along side their Shaman masters)
Yu Yu Hakusho (First work by the author of Hunter X Hunter, it's a fun series about a punk who dies, and has to work to get his soul back into his body)
Eyeshield 21 (American Football with crazy antics by a zany team of players, a must read, even if you aren't a fan of the sport)
to-Love-Ru (Latest series by the creator of Black Cat (But recently cancelled due to certain events *ahem >_>) and it's quite a funny harem manga to read, even if it isn't totally original)
Negima (A series about a ten year old British Wizard who is sent to Japan to teach a class of 31 beautiful girls, hilarity ensues!)
Hunter X Hunter (Awesome series, but unfortunately is plagued by hiatus)
Hellsing (Britain vs Vampires in the most badass way imaginable!)
Higurashi no Naku Koro ni (Amazing horror series that started life as a visual/sound novel, then turned into manga/anime/live action movies
Umineko no Naku Koro ni (Successor to Higurashi and
MY GOD IT IS EPIC, FUCKING, WIN! 
)
Ral Grad (Short series, rather enjoyable)
Rosario Vampire (Starts out as a monster of the week harem series, but it quickly evolves into something more, read the sequel series as well if you do read this)
GinTama (Funny as hell series, words do it no justice)
Gantz (Rather good series, not much else I can say about it)
Fullmetal Alchemist (Another Must Read, it's amazing)
MAR (Rather fun fantasy series to read, fairly short)
Saint Seiya (Knights of the Zodiac, This manga is rather rare though so you may have trouble finding volumes 1 and 3 if you plan on buying it)
Dr. Slump (Early Akira Toriyama, funny as hell)
Jojo's Bizarre Adventure (MUDA-DA!!!!! ORAAAAAAAAAAAAAAA!!!!!)
Claymore (Really cool series about Demons and Demon Hunters with Demon Blood, well worth a read)
