One year ago I was strong believer of the pseudo-fact that cartoons and animated media are for kids. There are many who believe in this pseudo-fact. Somehow, I started watching Detroit Metal City, anticipating that I will regret watching it. But, luckily it was just opposite. DMC became the first anime I watched and it was followed by death-note, Naruto, Bleach and many others. My point? Every animated movie or TV-series is not (only) for kids. There are many which explicitly target mature viewers.
This is the list of five Anime series based on corresponding Manga Series that everybody should give a try (trying to be a bit diplomatic here. should be read as must-watch).