That is right up there with "what is the meaning of life?" Everyone will respond differently.
I will share a few ideas::
1. Ensure your site complies to whatever coding standards you are using. For HTML, use the validator offered at http://validator.w3.org/
2. Ensure your site is optimized for SEO. Use an appropriate title tag, meta description and canonical for every page.
3. Social sharing is a component of web design. Facebook and Twitter authentication, sharing widgets, etc should all be taken into consideration.
4. Web security should be always be considered. Know which parts of your site will be public and private.
5. Know your audience. Who will use your site? A technical site may be designed very differently then a site discussing music or art.
6. Your site must be easy to navigate. Navigation bars, drop down menus, html site map, links, etc. all need to be considered. Buried content might as well not exist. Content should be layered so the most interesting content or best selling products will be on the landing page. Links will be offered so visitors can then move on to other products or content.
7. Stay consistent. I will take consistency over style any day. One example is breadcrumbs. There are some pages where they are helpful, and some where they are not useful. But if you decide to use breadcrumbs on your site, they should be used on every page so you stay consistent.
8. Check your site on every browser your audience might use. Presently IE 8, IE 9, FF 3.6, FF4, along with the current versions of Chrome and Opera needs to all be checked.
9. Go Mobile. Your site needs to consider the viewing screens of your users. Not only do you need to consider users with smaller monitors, but also the many users who will view your site from their cell phone.
10. Content is king. You can develop a perfect site, offer great security, and do everything else right...but if you don't add quality content then the rest doesn't matter much.
Wow. I had no intention of making it to ten when I started typing but the ideas just kept coming.