The golden ratio is great for print. But design for print and design for web are really quite different challenges.
You can layout a page of print with golden ratios all over it and it will look great for every reader. You can lay it out the same on a website, but then the users go and change the shape of their browser all the time.
As responsive web design is having it's day (and I'm sure something else will have the next day too), isn't it important to be flexible rather than rigid?
Jason Santa Maria wrote an article called What's Golden about this. I'll quote some of the relevant comments:
The rule of thirds and ratios such as the golden section are fantastic
methods for achieving designs that feel cohesive. The problem is these
principles don’t really apply to web design.
...
I’m not saying that using these principles is a dead end, what I am
saying is their usefulness is questionable for web design. The design
geek in me wants to just ignore the problems and push forward anyway
with a sly “I’ll still know it’s there.” And that might be enough for
some. But I’m not in favor of restricting content to a scrolling box,
or jumping through hoops to regulate the size of content, pages, and
browser windows. These methods push the problems on the viewers.
I’ve been beating myself up about stuff like this for years. I
originally came from a print background where ratios are a great
starting point towards unified design. It took me a long time to
embrace the fluid nature of the web and let go of that kind of
control. The best you can really hope for is leaving viewers with an
impression of the larger whole.
...
For a long time we’ve been looking at web design
through the lens of print design, and while some of the traditional
design practices can make the jump to the screen, some cannot. The
screen brings with it different kinds of challenges for visual design,
some of which occur exclusively in interactive media. It’s unrealistic
to think our old methods can fill in all the gaps, but new interaction
patterns and visual languages emerge everyday. These are the building
blocks for our new design principles.
However - this talks about the web design. But what about the content. If your content has imagery, by all means use the rule of thirds and the golden ratio in the photography for example - only here does the channel from print to web really allow such design rules to transfer unhindered. Similarly for logos, brand graphics and other 'untouchables'.
An image heavy website will perhaps look more beautiful if the images are themselves beautiful and the divine proportions that elevate one photo over an other will certainly have an impact on the appearance of your site because Content is King.
But in web and application design - very rarely does an opportunity present itself to be open to have such rigid design rules applied - in fact probably only in some minimal design where there are few elements in play and where there is an absence of any better design rules. i.e. divine proportions should almost be considered last when all other considerations have been taken into account.
So - best not to worry about it - leave it at the bottom of your toolbox - just in case you need it one day.