I enjoy Manga to a certain degree, but find much of it repetitive and/or boring.
Death Note is probably my favorite series, I've read all the way through it, and own all of the graphic novels that have been released in the US. For those of you who aren't familiar with the story, I actually wouldn't classify it as either Shonen or Shoujo. The story deals with Light Yagami, a genius high school student with dreams of creating a crime-free utopia. You essentially spend the series trying to decide weather you agree with the methods of Light (who kills off anyone who commits a crime) or L, the world's greatest detective. The story is very clever and intricate, something that I'm finding very rare in manga these days.
It isn't really Shonen, as Light the protagonist/antagonist never really shifts his original mindset, nor is it Shoujo, as there are very few relationships in the series, save the twisted friendship between L and Light, and Light and Ryuk.
I also read Naruto, though I'm not sure why, Full Metal Alchemist (which Ourchair has already detailed) and Monster, which I started reading at TwilightEL's suggestion. A few others I enjoy are GTO, Ranma 1/2 and Samurai Champloo.
Honestly I'm suprised to see that many of you like Dragonball Z, which I find to possibly be the worst animanga I've ever read/watched. No character development, a repetitive storyline, huge plotholes and empty and boring battle scenes make this to be a terrible series. Honestly, you have to be trying to make a manga this bad.