I hope this is a start of an interesting debate! I love this topic!
Great read: http://www.smashingmagazine.com/2010/02/09/applying-mathematics-to-web-design/
To contribute here with my own research. It’s not a well known fact and there are almost no images showing this on the web, so I made my own. It should be almost pixel perfect, if you dont believe me, try it on your own 

Sorry for a MSPaint quality… Hope you get the point of the image, I tried to make it easy to understand.
Another hard to find PDF document and great case example on a website :
www.freshface.cz/sneaks/phi.pdf
But please don’t think using a golden ratio is a holy grail. The holy grail for me is to have some kind of a system how I do things. You have to research and practice to make your own. You can then combine many things and the desired effect will still be there. These magic ratios could be a great start for beginners with web design, because it can keep the consistency throughout their theme. If you don’t have a system, you have countless of possibilities where to place elements and how big they can be. But if you will develop your own system/style, you can just grab a calculator and calculate like 1,2,3 possibilities, try them and then decide by eye which is better. This can significantly speed up your work flow 