It is very important that your pages be accessible by as many people as possible. The main problem with accessibility is that most people don't even realise it's an issue. Many clients who've asked me re-design their sites were quite surprised when I told them that their previous efforts were illegible by a huge proportion of their audience.
Accessibility has many facets.
One of them is browser compatibility. Your page needs to be legible under most, if not all, browsers on the market. This is one case where feature bloat really is a hindrance. Using the latest and greatest technology is a good thing, but often it means that you're cutting people off. This is not always the case, however.