I do it to keep my space a little more organized. I have a bunch of different pages in my root folder, and I don't want those mixed in with my wordpress files. Also, it's just easier for me when I'm updating things, and uploading. I do that a lot with my wordpress folder.
It's actually quite easy, and the way that I do it. I don't remember if 1.3 uses the same template system as 1.5, but either way it's similar. All you need to do is go to the wordpress options section. The first option section you reach is General. Under the option "WordPress Address (URI) put where all your wordpress files will be (http://www.my.domain/blog). Under the option "Blog Address (URI)" put the address to where you want people to see your blog (http://www.my.domain/). Then make sure that index.php is in the place where you want people to see your blog (http://www.my.domain/). If you're using a version of wordpress that has the theme system (meaning, if you have this folder wp-content/themes/..) then make sure that you use the index.php file that is in the root folder of your wordpress install. It usually looks like this..
/* Short and sweet */
Do not use the index.php in the themes folder, keep that where it is.
That's all you need to do. I know this works because that's exactly how I have mine set up.