There exists no way to cover all good manga, especially since people like different things. Forums are still good attempts, so I will try to contribute too.
There may be some loli (as in partially nude +middle teens) but no pedo stuff. Damn right biatches, some manga do contain child porn, stop denying it, that's just so goddamn annoying! "But the characters are actually older than they look!" Yeah, well don't we all get horny by the age numbers instead of the looks? ...Point made
First manga: da dA DA DRAGON BALL!!
Then One Piece...Comedy
Addicted to curry: A pervert/curry cooking master helps a friend's daughter run a curry house.
Great Teacher Onizuka: A gang member suddenly finds his call is to teach, but does it his own way.Psychological & thriller
Bloody Monday: Genius hacker+terrorism+dad's a special unit's cop
Death note: A top class student wants to change the wretched society around him, and finds the means in a book
Liar Game: A stupidly naive girl gets wrapped up in a game with 100 million yen debt, and asks a swindler for help.
Ikigami: Follows a man working for the government to hand out death notices 24 h prior the incident.
Franken Fran: A "strange" doctor does her best to fulfill the patients and clients' wishes, but somewhat lacks understanding of human thinking, and her abilities are too good for the patients' best (may belong to horror, but I still think there are some interesting chunks of psychology here)Action
Belzeebub: The most evil delinquent OF ALL TIME is chosen to raise the son of satan, with the aid of a gothic-ish demon nanny.
Shaman King:Ghosts do exist, and shamans help them pass on, or claim them as their spirits for varying uses. A japanese slacker is one of them weirdos, aiding both people and ghosts.
Veritas: A "dog" of the streets winds up at a school with martial arts and superpowers after his newly found master disappears.
History's strongest disciple Kenichi: A weak student wanting to learn martial arts meets a girl introducing him to martial arts
Ao no Exorcist: The son of satan chooses to become an exorcist.
Claymore: Akumas(monsters) lurks concealed among the medieval people in an unknown region, and half demon girls with silver eyes hunts them down.
Kekkaishi: Beneath a school lies Karasumori, a power drawing demon-like spirits close and making them stronger by the clock. Two clans destroy these spirits before they turn too strong, but that's a temporary solution.
Dragon Ball: A ridiculously strong boy secluded from society meets a girl searching for dragon balls, that when collected summons a dragon that makes any one wish come true. (I do not recommend Dragon Ball Z as strongly)
Nurahiryon no Mago: Youkai(demon spirits) roam in the dark, and the inheritor of a youkai commander position is three quarters human and wants to bee a complete one.
Blade of the Immortal: A girl seeks the thousand-man killer to help avenge her murdered family in old Japan.
Rorouni Kenshin: A traveling samurai with a inverted katana not meant for killing meets a girl whose dojo's sign has been stolen, in his name.
IF you haven't checked these out yet, well GET TO WORK
Naruto, One Piece, Fullmetal Alchemist, Fairy Tail, BleachHorror/action
Bitter Virgin (kinda the only shoujo I've ever managed to read through, drama with tragedy traits)
Record of a fallen vampire