Your Customers
This may seem obvious but is often forgotten. Beyond hobby sites, you are designing a website for clients rather than for yourself.
Whether buiding your own site or using a designer, adopt a moderate colour scheme and avoid personal foibles. Large, successful sites do so for a reason.
Search Engines
They do constantly try to improve capabilities but search engines are not good at reading many media such as flash.
If search is important to you, try to use accessible formats, with a few extras where they make sense.
An easily crawlable structure is key to the pages being understood, in terms of the code you choose and the physical layout.
Your Business
A common error is not to consider where a business is heading, only design for the present. Look to the future and avoid future cost.
Also ensure your site is planned to encourage visitors in the directions you want them to go. You wouldn't send a saleman out with no idea of how to close a sale.
We have no intention of outlining web design in one page, just a few aspects worth considering beyond design itself. The video on image optimisation for example, poorly configured images slow a web page and the user experience.
This is why Google are taking more notice of website performance, now a ranking factor. You may have seen the Site Performance section in Webmaster Tools.
Websites should be designed for users but helping Google appreciate and understand your site will increase visitors. Focus on quality and structure for your visitors, which search engines are also comfortable with.
This gives easy access to information and helps businesses increase their customer base. Few people complain about sites where they found what they wanted, even if the design didn't especially please but plenty take offence at slow, unusable, or off putting design, without bothering to look at the content.
Enjoy your website and be proud of what is created, you will maintain the site all the better for that but remain focused on the purpose.
The same principles apply to search engines and people. Website design is about your message, establishing trust and providing visitors with an opportunity.
Web design is a complex subject to briefly comment on. Looks can count but are not the purpose, businesses build websites for business. We share this aim and are always happy to help, you are welcome to contact us at any time.