PNG - Portable Network Graphics are not restricted to the 256 color limitation of GIF files and work well for images with transparent backgrounds as they have more options multiple frames and simple animation.
GIF - Graphics Interchange Format are possibly the most used on the web being used in logos and any other color images up to 256 color. For images that have text on them GIF tends to be better than JPEG as the files are usually smaller and JPEG tends to compress making the text blurry.
JPEG - Joint Photographic Experts Group the format is very popular due to its variable compression range. They can be used as High quality for photo printing, medium quality for web and low quality for attaching to emails. Jpegs are not so good for text as they can make it appear blurry so using them for graphs is avoided.
PDF - Portable Document Format is a file format developed by Adobe many desktop applications documents can be converted to PDF which allows for them to easily be viewed on many different machines. To view PDF files all you need is a free program from Adobe called Adobe reader.
PSD - PSD is Photoshop's native file format, It sometimes also goes under the name PDD. PSD is a widely accepted file format. And supports all available image types such as Bitmap, Grayscale, Duotone, Indexed Color, RGB, CMYK, Lab, and Multichannel. The biggest advantage of using the PSD format is that it can save images in layers (image, text, shape, etc.). This means you can edit an image one layer at a time and then go back to it at a later date you can also adjust and edit each layer independently to achieve better effects. PSD files are usually large because of the layers, but the size may be reduced by cropping the individual layers of the image. The maximum size of a PSD file is 30,000x30,000 pixels and may be saved with 16 bits per color channel. PSD image files may be opened with Adobe Photoshop or Photoshop Elements on Windows; and Adobe Photoshop, Photoshop Elements, or Apple Preview on Mac OS.