For me it would be Final Fantasy VIII or Metal Gear Solid 2: Sons of Liberty.

FFVIII - After i played Final Fantasy VII i really looked forward to Final Fantasy VIII and got really into the story of Rinoa and Squall and the flashes between Squall and Laguna.

Same goes for Metal Gear Solid 2 Sons of Liberty, Getting all the dog tags, Wigs, items, guns and finding out more of the story