Web image files can be categorised into two kinds, Bitmap-based (.jpg .gif etc) and Vector-based (flash, .svg etc).

Bitmap-based files are made up of individually coloured squares called pixels and are commonly used for photo-realistic images that require complex colour variations.

The most common bitmap formats on the web are GIF and JPG, although newer formats are slowly beginning to rival their dominance. Both use compression to reduce file sizes, so only save in these formats when you've finished editing your graphic - and always keep a non compressed back up of the original file!

Popular bitmap editors include Adobe Photoshop and Paint Shop Pro.

Vector graphics are made up of mathematical lines and curves and are generally used for illustrations, text and flat artwork.

Illustrator, Corel Draw and Freehand are some of the most popular vector programs, although they're not cheap. The cheaper Xara X is a worthy alternative.

More info: Vector vs. bitmap graphics.