PNG, Portable Network Graphics is a standard for lossless bitmaps supported by all modern browsers. Among its more notable features is support for alpha channels, i.e. partial transparency, which allows images to be anti-aliased (have smooth edges) and display properly regardless of the background color.
The only real problem with PNG images is that Internet Explorer prior to version 7 does not scale transparency to the web page background, but rather scaled towards the "background color" element that some image editing software can store in the image file. Most image editors pick a default color, often bright. One image editor that can select the background color to be used is the GIMP.
See also: The GIMP, JPG