Attack on Titan is an great anime and an even greater manga that updates regularly. The series isn't intricate as Naruto or Bleach's plot but it is (in my opinion) a lot better. The story centers around the life of Eren Jaeger and his adoptive sister Mikasa Ackerman, who live in a world where the remnants of the human population live inside cities surrounded by enormous walls due to the sudden appearance of the Titans, gigantic humanoid creatures who devour humans seemingly without reason. Their lives are changed forever after the appearance of a colossal Titan brings about the destruction of their home and the death of their mother, spurring them to enter the army to battle the Titans themselves.
Or If you want more "modern" interest, GANTZ right up there too. Heavy on the gore and despair. But with good reason. Gantz tells the story of Kei Kurono and his friend Masaru Kato who die in a train accident and become part of a semi-posthumous "game" in which they and several other recently deceased people are forced to hunt down and kill aliens armed with a handful of futuristic items, equipment, and weaponry. Both the manga and anime are noted for their heavy violence and sexual content.
Whatever your preferred manga/anime site is, it's more than likely available there.