It is not clear what exactly you are asking. Are you looking for a use case which requires more memory than can fit in the on-board memory of current GPUs (perhaps to demonstrate the utility of a new memory managing technique, compression technique, or a custom GPU board design)?
One use case I am aware of is business analytics (e.g. QlikView), which these days typically uses in-memory databases to facilitate real-time generation of results. As I recall, the minimum useful size of such a database is about 10 GB, which exceeds the storage of a single GPU of 6 GB.