The Casio Exilim EX-Z750, or Casio Z750 for short, is a  quite good ultra-compact camera. The Casio Z750's picture quality is just below the best in its class, with only a slight amount of corner softness keeping it from greatness. DC Resource found the pictures oversaturated by default but  adjusting the camera's image parameters solved the problem. On top of taking nice pictures, it does it fast and for a long time, thanks to incredible battery life. Other outstanding features include a high-resolution movie mode and manual controls which are quite rare among ultra-compact digital cameras. Weaknesses of this camera are few but mostly associated with indoor photography (flash, red-eye and LCD visibility). Unless this is your main type of photography, the Casio Z750 would be a good choice.

If traveling with this camera, consider buying the optional external battery charger (sold separately for about $50 USD) in order to avoid transporting the bulkier camera dock. The camera also has a handy voice recording mode. a triple timer for self portraits and several focus modes (pan, infinity, manual) of taking pictures rapidly without prefocusing. Just ignore the  bizarre features which this camera has plenty of.