In my kitchen I was running a microwave, toaster and coffee pot between two separate outlets on different walls. All three appliances shut off at the same time and there is no power at these outlets. The main ceiling lights are on and other lights in the room work, but anything plugged into these outlets does not. They are not GFIs. Both receptacles have six outlets.

Did you check your breaker or fuse? Some breakers are GFI so you don't always need to have it at the socket.