Yes. I like JRPG, Action RPG, and Action games. Can't play FPS' and don't care for straight up Strategy. I do like grid RPGs though.
If you want an action game that'll truly test your limits, Ninja Gaiden II can surely deliver on that.
The best JRPGs I've played were FFVII and FFXII.
Popular grid RPGs are games like Fire Emblem. The latest game for the 3DS received widespread critical acclaim due to its mix of western and eastern ideas.
My most favorite action RPGs are probably the Kingdom Hearts games.