In My Humble Opinion

Pay attention to user interface design. Look for readable color/background combinations. Craft your text into appropriate paragraph sizes. Provide consistent navigation buttons.

Make appropriate use of structural markup. Use headers as real section markers and not for font scaling. Make sure links are integrated into text flow (no 'click here'!). Make good use of lists vs. in-text enumerations.

Provide support for text-mode browsing. Put Alt attributes on all images. Make navigation possible without imagemap access. Content should all be present as text, not just displayed as graphics.

Cater to software agents too. You also need to be aware that not only people, but also 'robots' (e.g. from search engines) may visit your site. You can optimise for them too. In particular, you can use the META tag to specify descriptions, keywords, author, etc.

Create Legible Pages. Many sites have pages that are hard to read, and their designers don't realise it. What looks good on one monitor, with your eyes, may not look good on another, with someone else's.. The commonest mistakes are poor choice of background / foreground colors, and image detail interfering with the text. Many times I tried to use a starry background; but no matter how cool it looks some people may find it hard to read text on it. Don't assume that if you can read it, so can everyone..

Don't Keep Me Waiting. Another turn-off is those sites who keep on holding up pretty pictures for me to look at, and presumably, admire. If you keep me waiting too long, I'll go away. Keep in mind that many visitors (about a third I believe) surf with image loading turned off, or use a text browser, or cannot see well if at all, or aren't even human and couldn't care less (i.e. search engine robots). A really good test of a site's content quotient is to visit it with Lynx. The web would be dull if it was still as text oriented as when it was invented. But that stuff is only the packaging. Make sure you have some useful content inside it, and that people can tear through it quickly enough.

Don't Bury Your Content. HTML became so incredibly popular because it empowers us to communicate in ways previously only dreamt of. You get a real kick the first time you see your words and pictures nicely arranged on the screen - and you realise that your creation is available worldwide! Then you can go on to discover the power of Java, JavaScript, animations, etc... and the end result is that if ever there was something useful on your site, it's buried.

As important

as the visual aspects, there's also the more abstract ones such as navigation; structuring of content; use of language and other media in support of communicating ideas; etc. Navigation is important, especially for a moderately large site such as ours (500 pp.). I've occasionally had email to say they couldn't find such-and-such, please could I help - but what they were looking for, was perhaps only a couple of clicks down from the home page!

I pay extreme attention to the structuring of our site, even to the extent that I recently moved almost everything around to make it more 'logical' (IMHO)(I used symbolic links to avoid breaking existing URLs). The table on our home page is supposed to reflect that. I think of myself as more of a librarian than a graphic designer. Selecting and arranging suitable categories (as reflected by URL paths) is extremely important, to help people find stuff. What this boils down to is, choose your directory structure very carefully, and be prepared to change it as your site grows.