Lots of anime talk here, but if you want some real good manga here are my suggestions:
Vinlandsaga - Historical manga set in the High Middle Ages, great, amazing deep story about a young Viking warrior out for revenge. The story is told in the backdrop of a war, so there is lots of gore, blood/violence and such. but the character development, dialogue, art and realism is amazing.
Historie is also a historical manga, it follows the journey of a kid in Antiquity, who grows up in the 4th century BC and becomes involved with Alexander the Great. Graphics arent as polished as Vinland saga but the story is great and gets you into the manga real fast. If you like history you should try these last 2 mangas
Liar Game is a psychological manga, it is about this naive-ass girl who gets involved in this competition of wits; money is involved. Real mind****, each game is very well thought out and just when you think someone wins the game some new twist comes outo f left field.
Berserk is classic seinen, if you want to appreciate good old seinen with great art, fight scenes, etc. try it out.
There are many more but these would be my 1st suggestions. The main reason why I love this type of manga is that it isn't geared towards kiddies, where the main characters are like Goku in DBZ and their power level goes up by 500x and they face bigger and badder villains every 50-100 episodes yet they somehow still manage to beat them. oh yea and somehow through all that they are 100% pure of heart and extremely good and they fight for their friends and try their hardest to never kill and all that blah blah blah. The characters are a lot more realistic, they have flaws, and sometimes they dont get what they want.