Flash shadow created by lens
There are two causes of this problem. The most common is being so close to your subject that the lens of the camera blocks some of the light from the flash. This creates a semi-circular shadow or black area in the lower part of the image. That is what happened in the close-up of the flowers above. The solution is either to turn off the flash or to move the camera back and zoom in on the subject instead.
No lens shadow without flashThe other cause of a dark shadow at the bottom or side of the picture comes from leaving the lens hood on the lens when using a digital SLR camera's built-in flash. Even if you are an appropriate distance from your subject, the lens hood interferes with the flash, blocking some of its light and casting a shadow. The same effect can happen if you have a lens with a large diameter attached to the camera and fire the built-in flash. The solution is to always remove a lens hood or to change to a lens with a smaller diameter before using the camera's built-in flash.
For a great tip on how to avoid the black shadow from your built-in flash, read David Wells' article about Using Built-in Flash.