Years ago Sony patented a Full Frame curved sensor design for a fixed lens camera. They yet have to unveil such a product but in the meantime Toshiba and Canon patented such designs too:
The Toshiba patent looks like this:
The Canon patent proposes two variations. A fully curved sensor and a sensor flat in the center and curved on the edge:
A fully curved sensor would require the launch of a completely new system camera as the lenses would have to be redesigned. While the Canon sensor design with flat center and curved edges might work with current lens designs too.