Ghost Trick
Last Ranker
Ys (entire series)
Legend of Heroes (6 onwards)

Ghost Trick is a puzzle game/visual novel by the creators of Ace Attorney. You've just been killed, and as your ghost, you only have one night to solve the mystery of your own murder. This game has one of the best stories and some of the most mind-blowing plot twists I have ever seen.

Last Ranker is an awesome and highly unique Imageepoch RPG. Unsurprisingly, it was never localized. It has a very atypical (but good!) battle system and a somewhat unusual method of progression as well. It also has an incredible soundtrack by Yoko Shimomura.

Ys is a bit more well-known, due to the fact that Steam has given it some exposure. Nevertheless, it's still a pretty obscure series, and I feel it really deserves more recognition (as do all of Falcom's games).

Legend of Heroes is another series by Falcom. Unlike Ys, which focuses on intense action-RPG gameplay, Legend of Heroes focuses on story, character development and world-building. The series was pretty good through the first five games, with the exception of the horrible PSP ports of 3-5, which suffered a huge downgrade to the battle system. Bandai's localization didn't do them any favors either, as they were numbered and released in the wrong order and featured possibly the worst translation to ever exist. (I didn't have eaten a unusual today!) However, the sixth game, Sora no Kiseki, was excellent, and received an excellent localization by XSeed that didn't ruin anything. You may know it as Trails in the Sky. It even spawned its own series, which continued with Sora no Kiseki SC, Sora no Kiseki the 3rd, Zero no Kiseki, Ao no Kiseki, Sen no Kiseki, and Nayuta no Kiseki. Unfortunately, none of these have been localized yet, but they are all fantastic RPGs that deserve far more recognition than they get.