Liar Game (manga only) is a really good one if you're into tricks and strategies on a more "realistic" scale (not huge mechas having battles and what not). The manga is set up so competitors have to outsmart each other in order to save themself from reaching a great debt and earning a nice profit for their own use. Akiyama is the real backbone of this manga for me, I'd say that his plans are more enjoyable to watch than even the more notable characters like Light and Lelouch.
Monster (manga and anime) is also a great one. Johan (the one in my signature), the antagonist of the series, is a very neat character. This whole series tries to stay in the realm of reality with possibly the exception of Johan since he's supposed to resemble the anti-Christ. The main character does his best to stay true to his morals, but sometimes it's not always easy. This series rotates around Johan as you might expect; he's the "monster" of this story. His backstory is the main mystery.
20th Century Boys (manga only) is made by the same person who made Monster. This is often known as Urasawa's "masterpiece". I have to say that the theme of this manga is possibly the greatest I have yet laid eyes on. The mysterious cult led by Friend automatically draws people in. It's easier to read than Monster, but both can be pretty tricky if you're new to this genre of manga (eg. if shonen fighting styles are your only enjoyment).
