Rottie,
I think that a lot of people feel like the harness is gentler to the dog, so their neck doesn't get the strain when they pull. I can just see mine in a harness pulling me all over the neighborhood though! Ha Ha!
A lot of people who I have met on the MSN Golden Retriever site have used what is called a Gentle Leader, with a lot of success. I think it prevents the dog from being quite so mobile, but I've never seen one used, and I know it wouldn't work with my obedience trainers as they are quite strick about equipment.