In HTML (and older browsers like Netscape 4.), it’s just a matter of adding border="0" to the img element.

In CSS and the latest browsers, all you need to add is the following rule:
a img { border: none; }

You can make the border invisible using CSS in Netscape 4.x by changing the border colour to match the container’s background colour:
a img { border: none; border-color: [background colour]; color: [background colour] }
So, on a white background the color properties would have a value of white. This will still leave about a 2 pixel space around the image in Netscape 4.x.