GIFs cannot have alpha transparency. So you need to choose the same background color as you use on the HTML page, so that Illustrator can calculate your graphic when saving for web.
PNG can have alpha transparency, but you cannot use the "screen" blend mode in it.
Thanks for the response. Unfortunately, this logo will need to be placed over another image so I can't really use the same background color. Do you know of a way I can make this happen or am I out of luck with the glow?
You could choose an average color. If that's not possible you could put the logo into the background image. If you need to have it separate (in order to make a link or something) you can only make a PNG. But be aware of IE 6. You have to use tricks like Dean Edwards IE7 script to make it work.