I don't watch too much anime, but I'm a huge fan of the anime Detective Conan. It's about a teenage detective that had a run in with two assassins. He was defeated and force-fed a poison that was supposed to kill him. Somehow it doesn't kill him, instead, it reverts him to the physical age of an elementary school kid. Living with his childhood friend and her bumbling detective dad, he has to track down the assassins and take them down. While doing that, he also helps solve murders, thefts and other shit.
Unfortunately, not only did Funimation cancel the English dub, they also threatened to sue a group that was fansubbing the remaining episodes. The dub stopped at episode 90 while the show is actually still continuing past the 700's.
I've always have been a mystery-nut, and it's hard to find any mystery genre anime out there.