Looking at websites from a coding rather than 'looks' and 'content' point of view most are poorly designed and almost none comply to any form of accessibility.* A well designed website will work in most browsers, I've done websites that conform to XHTML strict, CSS and WCAG AAA** and can be viewed in Firefox, Opera and IE with only slight problems in IE (larger space on the left than right of centered page, but otherwise fine).
To design a complient website just use the correct tag for the correct job
<p></p> defines a paragraph, not a "big gap"
<h1> is a heading, not big text
<table> is for data not layout
use width, height and alt for images
use relative font sizes em or %, not pt and px
don't use colour or images to convey information (obviously excluding graphs, charts etc.)
Use <label for=""> for forms
don't rely on javascript to make things work
Include document type declerations
Use CSS for layout and design, it can be a bit funny with I.E. but only if you abuse 'float'.
I'm working on a new NUCC website, the old one is crap and as Chris rightfully says "Just include everything, dammit" but if you compare
http://www.su-web.nottingham.ac.uk/~caving
and
http://www.incendiumhq.biz/ (temporary testing location)
excluding the different colours they are pretty much identical, when the new site is finished they near enough will be, apart from the back end "admin area" the front end is only different in that the new one is compliant to WCAG AAA, XHTML and CSS and the old one didn't make WCAG A, HTML or CSS. The new one does do some odd things in IE but it's not fully debugged and half the links don't work, when IE 8 comes out, they've said they'll fix these problems.
I'm impressed with the UBSS site as it coded well, although the menu appears halfway down the page when viewed with CSS turned off. (Haven't checked a lot of sites, just Chris said it was the best one so I tried it)
How many of you can validate your website and not get an error with:-
http://validator.w3.org/
http://jigsaw.w3.org/css-validator/
I recommend using firefox for coding as you can get some ace extensions that really help with layout (especially css).
https://addons.mozilla.org/en-US/firefox/addon/1843
https://addons.mozilla.org/en-US/firefox/addon/5809
https://addons.mozilla.org/en-US/firefox/addon/2318
*ok so the chances that blind people, people without hands, cerebal paulsey, etc. will visit your site is limited. But I've spent idle minutes clicking away on wikipedia and ended up looking up crap, why should they be prohibited, hell I'm on this forum?
**http://www.w3.org/TR/1999/WAI-WEBCONTENT-19990505/