The first time that I felt I was playing something truly unique was probably when I started playing Earthdawn. This was a move from Shadowrun which seemed to be a game-changer but I felt it was still not truly unique. Earthdawn made me look at fantasy in a completely different way.
Earthdawn took a completely new look at Fantasy and as I held the first edition in my hands I felt it was truly unique. It took the tropes of Fantasy and reworked them into something new. It was also the first game that I truly felt the system assisted the storytelling. I truly felt that the rules added to the feel inside the game. It was as if they considered the rules to make the player feel what it may be like for that character to handle its magic in the game.
Also, consider that it seemed to have a class-based system that was driven by skills. This may not have been totally unique at the time but it was unique to me. I am not a major proponent of class-based systems but that game has gotten it right. That combined with the whole horror/fantasy setting that was beautifully crafted meant that this game truly sticks in my head as a brilliant game. Keep rolling!