#5 - Death Note
Like any great story, Death Note builds itself up from a simple concept and keep going from there. Light Yagami, the most brilliant student in his class, happens upon a mysterious notebook that reads "DEATH NOTE." Inside the book are many rules - and one of them says "The person whose name is written in this notebook shall die." There are many other rules and cool stuff surrounding the Death Note, and I'm not going to spoil them here.
Light takes the notebook home with him thinking its a prank notebook. He sees a criminal on TV attempting to kidnap a bunch of kids for ransom, and writes the criminal's name in the notebook. 40 seconds later the kids slowlt file out of the school safely, and the news announces that the kidnapper has suddenly collapsed and died. Light looks in terror at the Death Note, realizing what he has done. Over time, Light decides to use the notebook for good instead of evil, and he starts killing criminals with the notebook. Criminals in prison are dying of heart attacks by the hundreds, and everyone is noticing that there is no way that these deaths are a coincidence. Someone is murdering these criminals, and the ICPO has declared the person responsible a serial killer.
Light is watching this unfold from afar... continuing to kill criminals and watching as the news and investigators are baffled and terrified. And then the ICPO brings in their trump card... a detective named "L." L is the world's best detective. He has never lost a case and is only called in for the most heinous crimes and mysteries. L lures Light into a trap on live television and narrows down Light's location to Japan's Kanto region. Light is now considerably less safe than he has been in the past, and decides that he has a new objective - to kill L. But L's secret identity prevents him from being killed by the notebook. Likewise, L cannot press charges on Light without first exposing him as the killer and finding out how he kills.
The above dynamic drives the entire 37 episode anime. It is Light versus L - each with their own idea of justice. Its a true thriller detective story, mixed in with the dark moral ambiguity, the gradual unfolding tactical battle between Light and L - even going as far as having them meeting and both working along side each other to catch the killer - but Light cannot kill L without knowing his true name, and L cannot prosecute Light without proving that he is the killer. The first one to be found out dies.
I cannot recommend this anime enough. It stands out as a gem of realism and thought provoking, thrilling, cat-and-mouse storytelling in an ocean of cliched anime.