Image file type depends upon a few factors. The simplest way to work out what file type to use for what image is, if it contains many colours use JPEG, if it has a small palette of colours use GIF.
programmer is right but if you need advanced level of transparency then png is the best then you can have a true color image with transparency and alpha, like shadows but the problem with png is that it is not supported on IE6 - and needs a css hack or java script.
It is really based on what is the requirement. But if you will ask that if in the same requirement which should be chosen then I say it is JPEG, best compressed format and load much faster then any image format.