@Qemo 91 Days - mafia/detective style anime. MC basically joins mafia to find who killed his family. really good. beautiful bones sakurako's investigation - this is detective style anime but its about using bones to find clues rather than normal stuff aka anthropology. still really good. erased - extremely good mystery anime. there is supernatural stuff in it where MC goes back in time to basically be a detective and find out what happened and what led up to the present events and to change it. acca:13 territory inspection dept. - highly recommend this anime. mystery anime but the MC is basically a detective
Death Note and Code Geass. Both have some fantasy element to it, but the underlying theme is the intelligence of the characters, and their use of it.
Although it's not anything close to realistic, I would have to agree with a few prior posts and suggest watching Death Note. It's the first anime to come to mind when I think of a detective anime.
Death Note, Zankyou No Terror, Code Geass. One Outs (not a detective anime but very very intelligent$