Lunar Silver Star Story - http://en.wikipedia.org/wiki/Lunar:_Silver_Star_Story_Complete
I think an under-rated RPG and far better than a lot of bigger named ones.
Heavy Rain - Just engaging storyline - closest to a movie feeling
Flower - One of the most peaceful, engaging experiences I've ever had with a video game. Loved every second of it.
Metal Gear Solid - Really engrosses you, if you let it. Some of the most engaging games I've ever played. Loved MGS2.