I'll second Phenomeno and Umineko as they fulfill all 3 genres.
For thrillers, you can't go wrong with G-senjou no Maou, though not much of a mystery.
Remember11, 999, and VLR are good thrillers too, with atmospheres which can creep you out in some bad endings.
Shikkoku no Sharnoth is horror mystery. It's slow-paced, but the prose more than makes up for it, unless you dislike it.