ID: Invaded was very fun and definitely one of the better originals from these past few years. Also, since it hasn't been mentioned yet, Odd Taxi was well-liked by those who watched it as well.
Monster is a classic. It's a more western-style thriller/drama with a very aesthetically pleasing art style (I love Naoki Urasawa ♥️). The central mystery is super compelling and the conclusion is satisfying.
Mononoke is a very weird procedural detective show. The fansubbers who subbed it originally included cultural notes with the episodes even lol, but it's certainly a Ride.
It's arguable whether it counts, but I love me the Monogatari Series (starting with Bakemonogatari). It's my favorite ever. The characters are some of the best in the medium. Awesome character development and the chemistry between characters is great. And though I don't think it comes up very often when the show is discussed, it /is/ supernatural mystery show, with most arcs focusing on a central mystery. The writing is pretty tight throughout the entire series and only gets better. Although, uh. Nisemonogatari is, imo, a low point against the rest of the show.