Print Graphics: TIF, AI and EPS files are the best choices for professionals when images are intended for print. Its ability to read CMYK and YcbCr color, plus its ability to store such high pixel intensity makes it the only choice for designers, photographers and publishers.
Web Graphics: PNG, JPEG and GIF are the most web friendly image formats. JPEG is great for images when you need to keep the size small, such as when you need to upload it online. If you don’t mind compromising the quality of the image a bit, use JPEG. If you want to keep the size small, but still retain the image quality, use PNG. GIF is the worst choice, although file sizes are very small, and they load very fast. Plus, if you want to add animation effects, use GIF.
PC & Mac Compatibility: If you are using Mac or PC, or constantly shifting from one to another, JPEG is the best image format for PC and Mac Compatibility.
Logos & Line Art: JPEG is the worst choice, it tends to add artifacts and blur the text, line and edges. JPEG also cannot support transparency, which is often a need for logos or icons. GIF is a good choice, but it pales in comparison to TIFF, PNG, AI and EPS. Both of the latter image formats retain much image information, and are not limited to 256 colors, unlike GIF. TIFF and PNG files keep the logo or line art sharp and concise.
Clip Art: GIF is the best image for clipart and drawn graphics that only use few colors and precise lines & shapes.