My Top list:
.TIF (can support layers, high-resolution, high-pixel-density stuff)
.PNG (Easy to use and high quality)
.BMP (not bad)
.SVG (VECTORSSSSSSS)
.GIF (You need a good program to make animated GIF high-quality, then it's still washed-out)
.JPG (uses too limited, i.e. just photography)
Anything I forgot?