• If the images are for the Web or online, use JPEG, PNG, or GIF.
• If the images are for print, use TIFF.
• If you want to keep a version that remains editable, choose your software's native file format. (PSD for Photoshop, PSP for Paint Shop Pro, CPT for Corel Photo-Paint, etc.)

Here are brief descriptions of common graphics file formats, with links to follow for more information:

JPEG - JPEG is best for photos when you need to keep the file size small and don't mind giving up some quality for a significant reduction in size. JPEG is not suitable for images with text, large blocks of color, or simple shapes, because crisp lines will blur and colors can shift. Only JPEG offers the options of Baseline, Baseline Optimized, or Progressive.

• Baseline (Standard) - This JPEG format is recognized by all Web browsers.
• Baseline Optimized - This JPEG format option provides optimized color and slightly better compression. It is supported by all modern browsers, but was not supported in the very earliest of Web browsers. It's your best choice for JPEG files today.
• Progressive - Creates a JPEG file that displays gradually as it downloads, starting out blocky, and gradually getting clearer as it downloads. It doesn't make the image download any faster, but it can give the illusion of speed since the blocky image is loaded right away on a slow connection. With the majority of internet users on high speed connections today, Progressive JPEG is rarely used.

TIFF - TIFF is good for any type of bitmap (pixel-based) images. TIFF produces large files, but there is no loss in quality. TIFF also preserves layers, alpha transparency, and other special features when saved from Photoshop. The type of extra information stored with TIFF files varies in different Photoshop versions, so consult Photoshop's help for more information 

PSD, PDD - PSD and PDD are Photoshop's native format. Use PSD when you need to preserve layers, transparency, adjustment layers, masks, clipping paths, layer styles, blending modes, vector text and shapes, etc. The PDD extension was used in Adobe PhotoDeluxe (now discontinued), but it is identical to PSD format and the two can be used interchangeably.

BMP - Use BMP for any type of bitmap (pixel-based) images. BMPs are huge files, but there is no loss in quality. BMP has no real benefits over TIFF, except you can use it for Windows wallpaper.

PICT - PICT is an old, Mac-only bitmap format, similar to BMP for Windows. PICT is not often used today.

PNG - Use PNG when you need smaller file sizes with no loss in quality. PNG files are usually smaller than TIFFs, in my experience. PNG also supports alpha transparency (soft edges) and was developed to be a Web graphics replacement for GIF. Note that if you want to retain full transparency, you will need to save your PNG file as PNG-24 and not PNG-8. PNG-8 is useful for reducing the file size of PNG files when you don't need transparency, but it has the same color palette limitations as GIF files.

GIF - Use GIF for simple Web graphics having limited colors. GIF files are always reduced to 256 unique colors or less and they make very small, fast-loading graphics for the Web. GIF is great for Web buttons, charts or diagrams, cartoon-like drawing, banners, and text headings. GIF is also used for small, compact Web animations. GIF should rarely be used for photos.