well actually, when you compare google and facebook and semilar websites you will have to take into consideration that they provide of the hook service no one else provided before them, and this service requires fast processing mainly, which is done by simple designs, but:

With periority:
1. Functionality
2. tech
3. visual design

If you are providing a rarely offered service, then the looks is not really important tho it should be elegant, like fb its simple in design yet elegant.

If you are providing a service that are offered everywhere else then you shoud concentrate on the looks and the backend, backend will give you a plus.

In Brief and recommendation:
Visual looks is so important no matter what, nowadays it gives a huge professional look and impression, I have been a webdesigner before i switch to system adminstration for about 6 years, and my simple advice: Looks count, at least it will be memorized, not to mention its alot easier to accomplish than off the hook services.
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Visual design often makes a product more usable, for example: If it looks good, you probably have a good overview. If you go to Google.com it doesn't look very special, but it does look good. It's clear what you have to do. Mahalo on the other hand (before the redesign) was a MESS, a real mess. all those lines on top of the categories with *new this* and *new that*. It's just not inviting. Kudos to Mahalo for the redesign.

visual design/appearance - 10%
UI/functionality/easy to use - 50%
technology/back end - 40%
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First and foremost, web design should be about usability and accesibility. It's where you put that button, that form, or that textarea that matters, and only after that "how it looks like".

Those percentages change based on the purpose of the website. If it's a technological demonstration, then the user is a techie, so it would be Visual 1% / UI 19% / Tech 80%. If it's some cool artistic portfolio, the measurements change like V 70% / U 15% / T 15%. A big project like Mahalo have these percents split equally, because they are covering a wider range of people.

Overall, I think the more technical-oriented you are, the less you care about visual design. The more artistically oriented you are, the more you care about how the site looks like, rather than what it is build upon. For the average user, looks come first, then usability, and only after that the technology, so an average would be V 60% / U 30% / T 10%.
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It can't really be broken down without consideration to the product/business/ service since those will be the primary factors you'll need to consider.

The empahsis that you place on the things you listed is really going to depend on 2 main things:

1. Your user (what will they respond to and what are their expectations)
2. What action you want them to take.

Google is nice and simple, because users want to do one thing, so their interface doesn't not hinder it in any way and meets their expectations.

If you were going to a salon website or an interior design website, more of a visual emphasis would be expected since that site is primarily selling an image itself.

Technology and back-end factor into the tasks and making it as easy for the user and getting the results they are expecting. Whatever it takes to help you accomplish that would be dependent on the goals.

I wish it could be more cut-and-dried, but it'll really depend on what you need to do.
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Being a web designer myself, this is how I designate it:

visual design/appearance - 100%
UI/functionality/easy to use - 100%
technology/back end - 100%

Just a year ago, you could have reduced the visual design/appearance of a site and still been extremely successful. That was "web 1.0". With this new "web 2.0" thing, i.e. pretty web pages, no one will stay at your site for very long if it's not themed correctly by color scheme and layout. Therefore, without a good look, they won't say, so looks is 100% important. (Ignore the exceptions, like craigslist. They are a very special case.)

But if it's not easy to use, and things can't be found easily or they are not where they should be, then they won't stay nor bookmark your site. So organization, functionality, and ease of use is 100% important. (Craigslist is 200% easy, so they don't have to look pretty.)

Lastly, the technology / backend is most important for me. I didn't have one before. I literally constructed every single page by hand. Then I constructed the back end, and I was able to increase the size of my site one hundred fold with valuable content in a matter of days. Without a good back end, your site will be exhausting and a mess. You'll quit before you make any good money. So back end is 100% important.

Also important: your site has to either be something search engines will like, or something people will readily bookmark. Without one of those two things, you won't do much.
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There's a great principle: Form Follows Function. If the design element isn't there, the site can be difficult for users to use, even if nothing is broken. If the first-time user can't easily figure it out/find what they're looking for, they'll be back to Google trying to find something else.

So it's pretty important, but obviously everything needs to work first. I'd say that your first two categories need to be combined, because the visual design is part of what makes it easy to use. So that said, I'd say those two categories total 50% and back end 50%.
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Visual Desgn/Appearance: 10%
UI/Functionality/Easy to Use:70%
Technology/Back End: 20%

I believe it's extremely important - but not in the way that many designers seem to think (therefore I gave it a low percentage).

When the majority of users went to broadband, designers saw an open door for being creative - not being limited by what had to be downloaded by dialup. So many websites are now "too clever" for themselves. Functionality is down the tube. What should be obvious buttons like "Home" and "Contact" are often buried or very small.

While we all like things that look good, few would argue against this statement: In the end, we want to pull up a site, do with it what we visited it for, and move on; not sit back looking at a hard-to-use page but that looks pretty. Those pages, we visit as few times as possible.
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well, i will give you a small comparison to get you going
compare: cuil.com vs. google.com that should give you heads up on looks vs functionality
Also compare: hi5.com vs. facebook well facebook has both hehe
compare: geekstorage.com vs. dreamhost.com

tho dream host is older and bigger, but from the looks you get the feeling that geekstorage is alot more progessional
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Absolutely important. Search engines might help you get traffic because of your content, but it's your visual design that keeps the user onto your website. If the layout is not good, he might leave from the landing page itself, and that'd result in a high bounce rate for you and thus less conversions.
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I speak as a web designer.

Visual design *is* very important, but there are two things you should understand. One, visual design does not necessarily mean complex design. Two, there are two aspects to design: information design and graphic (visual) design.

Information design comes first. The designer looks at what the web page needs to accomplish, and then they lay out where everything needs to go in a way that is most usable. Once everything is positioned as needed, it's time for the graphic design to begin.

The graphic/visual design part is where an artist takes the page layout and makes everything in it look as nice as possible. His job is to make the existing layout most readable to the end user, and he makes the most out of the page design. Sometimes, less is more, where heavy design elements are not needed and would in fact detract from the overall design. Other times, graphics are more important to aid the user in completing a task.

For example, a web project I'm designing, www.rmberit.com, allows users to make online notes for them to use, edit, and refer to on the go. (Note: If you want to use it, you should know that it's functionality is not yet complete. It's just an example.) This is a simple function, so the page design is relatively simple, but at the same time there are graphical elements I felt were important to help the user know what to do (i.e. the stickies give the user a real-world metaphor so they know what the site's about).

Google has a very simple function: search. All someone needs to do is type in a box and push Google Search. This is front and center. Since the site has such a simple and limited number of functions, there is no need for complex design. Its information design calls for this simple design, and the visual design part simple results in a nice looking logo with a non-distracting way to access other services. And since everyone already knows what Google is, they can leave out extra design elements like a magnifying glass or whatever. Cuil.com is another example, but the background is simply black instead of white.

Another example is apple.com. Their web design is simple (information design) and clean (graphic design) that produces an easy end-user experience.

And as your breakdown goes, it might be something along the lines of:
visual design/appearance - 30%
UI/functionality/easy to use - 60%
technology/back end - 10%

So short answer: good visual design is important, but sometimes great visual design should not even be noticeable.
Source(s):
Experience, Web Design for Dummies

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50% - content
25% - design
25% - function

A site with poor, incomplete or out of date content isn't worth visiting.

A great visual design needs a good functional implementation, otherwise it's just eye candy.

A functional site will suffer if the design is ugly or confusing.
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The percentages for these factors are different for every website and vary depending on the goals a particular website wants to achieve. For example, in the case of Google, I would suspect the following numbers to have been considered:

technology/back end - 50%
UI/functionality/easy to use - 40%
visual design/appearance - 10%

In order for Google to achieve and remain the largest and fastest overall search engine in the world, the back end technology must first be open-source in order to allow customization and flexibility for talented programmers to build proprietary logic that can exceed beyond commercial closed-source out-of-the-box technologies. Adequate search functionality comes next while visual design comes last. Because excessive visual design can reduce search performance, only practical and simple solutions are considered in order to remain with acceptable constraints.

Apparently, not all websites are out to be the best search engine, thus percentages for these factors will obviously be different.

Hope this helps!
Source(s):
App & Web Developer

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visual design/appearance - 20%
UI/functionality/easy to use - 25%
technology/back end - 55%
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visual design/appearance - 40%
Websites that are pleasing to the eyes, not causing strain or whatever are preferred by users. Today, users like websites that conform to Web 2.0. Designs that have shiny and shadowed effects like that of Windows Vista are pleasing to your visitors. If you have good design, they will keep coming back to your website

UI/functionality/easy to use - 40%
Like visual design, this criteria is also considered by your visitors. To do this, make sure that your website is computer-independent. Meaning it runs the same way on different machines with the same function and ease of use. It should run the same way when users use it in opera, firefox, ie, or if they are using linux, mac, or windows.

technology/back end - 20%
This is not so important for users but this is important for your programmers or web designers because the stability of your website is measured through this. I mentioned about Web 2.0. Usually, pl used by web 2.0 programmers are ajax, php, mysql..
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