By simply looking at Sony's PlayStation 3, for example, you can see a number of videogame franchises that are decisively "PlayStation" in that they are automatically associated with the PlayStation brand. They help set the brand apart from its competitors in a way a multi-platform game can't.
Exclusives offer an experience that is especially unique to the platform. The game is designed, styled and built around the functionality of the console. Do you know of any Gears of War-like titles on PlayStation 3? What about an Uncharted-esque game for Xbox 360? These games are centered around exactly what the console offers in terms of development capabilities.
It's been a fantastic generation for new and exclusive Sony IPs and there is absolutely no shortage of upcoming exclusive titles for the PS3. But which unique IP has thrived the most on the console?