PNG - Allows for transparency but won't enable you to create animations. Its mostly used for Rendered images.
GIF - is not a lossless format which really means that every pixel is preserved when it is saved. It also allows you to create animations. Mostly used for animated Avatars
JPG - is a lossy image and is mostly used for Photographic images as although it compresses the image, it allows you to alter the compression. Widely used to create wallpapers, signatures and banners.