Web Standards
This entire site conforms to the XHTML 1.0 Transitional and CSS 2 standards. It renders usably in every browser I've thrown it at including line-mode browsers like Lynx. For more information on the benefits of conforming to web standards please visit the Web Standards Project.
The Designers' Challenge
The concept of standards must be sold to clients and organizations. It is our duty to evangelize these things and show that it's not just a convenience for us but a smart business practice. The concept of a web site as a stack of paper that will look the same in every situation is still prevalent.
A better analogy to use is that of other electronic communication media. Music publishers equalize and compress their product so that it is listenable on everything from a $40 Aiwa boombox to a $20,000 audiophile system. Television broadcasters still keep the primary content of their broadcasts out of the extreme edges of the screen so that even on a black and white from the '50s will still be watchable. What do they know that many people on the web don't? A wide audience is the easiest route to success.
It's Not Just About the Web
User interface standards and common design patterns have an important role to play as well. If you're introducing an entirely new concept to a user the more familiar things you can show them the more likely they are to interact with the things that are new. There's a dangerous meme of "engagement" in our industry that assumes that if your interface is novel and "fun" enough users will tolerate inconsistency and confusion. This is only true if no other interface exists to accomplish what the user is attempting to do and if a user is seeking alternatives the first time they use a product something has gone wrong.
Lead by Example
As designers the best thing we can do is to practice what we preach. There are many folks who like to talk about these things as academic exercises (and are very good at that) but don't follow through in their own stuff. If done correctly a well-formed site can not only look better than a messy table-nested equivalent but will support every browser ever made.
Where to Begin?
Here's a few web resources that were extremely helpful in my own transition:
