What is the best image file format?

There is no single best image format. There are many very useful formats:

JPG - easily used in web pages and shared. However, JPG files are compressed and therefore lose some of the image quality.

DNG - see raw formats.

TIFF - a complex format largely used in scanners and faxes.

RAW - RAW files are not standardized between camera models. They have an advantage in that they keep intact everything recorded by the camera but they are large and not easily shared or printed.

There are about 30 more commonly used image formats.