Hah! This one is easy.
Just add the
border="0" paremater to your img tag.
Your html tags may be something like this:
[img]image.jpg[/img]
If you omit the width and height it will default to whatever actual width and height the image has.
By specifying the border parameter you won't have the blue border around it (or other color, whatever it is for links in your web page set up).
It doesn't matter if your <a href=....> tag points to a web page on your site or elsewhere or the [img]...[/img] refers to an image on your site or elsewhere. The principle is the same.