I think that for a website to be a success it must meet the users expectations. When i click onto a search result, what do i want to find ? It must be user friendly, aesthetically pleasing (not so important), and it must have the information i need. What else do you want from a website ? What don't you want from a website ? eg., bags of clutter and chaotic navigation.
It all very much comes down to what side of the website you are sitting but I would first and foremost say: Usability. Make your site usable I will return
I would agree with all the above but would also say that "aesthetically pleasing (not so important)" is wrong, remember this is your shop front to the world, if you think about a high street, if your shop front looks derelict and un inviting will anybody come in, same applies for your web site. IMHO
It should look as professional as some of the better sites in the niche, with immediate visual cues as to what it's selling. It should let people get what they want, easily.
it really depends on what you will use it for. is it just an website to provide information about your products and services, an ecommerce site or a blog.
Simple to use, appealing to look at (not necessarily ornate, but not ugly) - and functional. Needs to do something useful and to do it in a straight-forward fashion, working well and working consistently.
Usability (easier to get round) Design/aesthetically (well chosen font, colour, spacing) Content (essential information should be easy to find.
It really does come down to the aims. For the user? ease of use? information? For the webmaster? Conversions? CTA's?