Hmmm ... well ... if mind-games are your thing then ... let's see:
There's Umineko no Naku Koro ni - which is a spin-off of the Higurashi series, and it's all about the protagonist outwitting an opponent in a psychological game where everyone's lives are at risk. It's light on action, and falls more into the psychological thriller genre. You can actually watch Higurashi no Naku Koro ni and it's sequel Higurashi no Naku Koro ni Kai as well - similar concept, although I would advise you to pay close attention because missing something means losing track of what's going on. In the case of Higurashi I would recommend watching both seasons back to back if you can manage it.
Next up would be Paranoia Agent - I haven't gotten around to watching it yet, but apparently it's quite good as well.
Hell Girl (Jigoku Shoujo) may also be worth watching, but the pacing is quite slow in terms of plot development, which I've found in the past puts people off a bit. There are 3 seasons, with the final season arguably being the better of them.




