Triple Triad - FFVIII
The greatest minigame ever conceived, and it was so good that Square actually made a stand alone version of the game. Too bad it was only released in Japan. It's so good that fans have made their own version of the game to be playable online, such as Triple Triad Extreme and a PSP version of the game which is shown in the screenshot below:
Although TT doesn't have a relevance to the main story, I've heard many people commenting they could spend 'hours' with the game just playing TT, perhaps spending more time with TT than the actual game. FFVIII is my favourite FF game so I'm implying FFVIII is crap or anything.
Square even tried to mimic TT's success by creating another similar minigame in FFIX, Tetra Master. Unfortunately, it was overly complicated and wasn't as fun/good as TT.
Jam it back in, in the dark.