1) Number one thing is always content. If you have good information or data available on your site, the rest can be sh*t and people will come there anyway. Good example is a student website of my university, where students put their study materials and teacher/course references. The design is ugly, it is slow as hell, it is infested with ads, but everybody uses it anyway.
2) Accessibility it the close second. Your website should be accessible for both users of any major browser or platform as well as search engines indexing the content. Good practice is to optimise for sight impared users that use screan readers. There are plugins that simulate that for FF. You should aso make sure your site degrades gracefully, that means it should work properly without javascript, css, images and any combination on those. The content is useless if people can’t get to it or read it properly.
4) Usability is the next important thing. You should help your users find the information they are looking for or help them archiev their goals faster, safer and make the process altogether less stresful. You can use javascript for drag and drop features, or AJAX search suggestions, etc.
5) Your site should be secure and should use privacy standards. You should not expose your users to security risks or they will lose trust in your website. This is especialy true for any e-shop sites or any sites that deal with money and personal information.
6) I am a graphic designer, so I have to mention a good ‘working’ design. Deasign should make users of your website feel in a certain way. News portals want for exaple their users to trust the news, so they employ pastel blue palette and clean well-arranged synoptical design. Luxury is also a goal of many website designs.
To sum it up, your site should have a good quality content which is easily accessable to most users and search engines and user friendly UI which makes the visit the least stresfull and makes them feel in a way that makes them trust the quality of the content or product. You should use security and privacy standarts to ensure the trust of your users.
I know that you asked for something a little bit different, but I just felt it should have been said, especialy to a starting webdesigner such as yourself :-)