Web developers should be designing their pages to be accessible, not just with the latest technology, and the browser you view pages with can impact how you want to develop. Plus, many of the newest versions add in features that may be nice, but aren't ultimately supported (e.g. Netscape layers). Here you will find suggestions on how to change your browser intelligently.
Accessibility
There is more to accessibility than the browser, but this is the most common way for a site to be inaccessible. "This page must be viewed with XYZ Browser." Readers who see that message are not going to upgrade their browser, instead they think "what a lame site," and move on. And it's developers who expect everyone to use the same browser they use that cause this problem.
Why Upgrade?
Moving to an up-to-date browser can have some benefits. The newer the browser is, the more likely it will take advantage of the latest technologies. You can then use them on your own site, and you'll be seeing these effects on the sites you visit. Plus, the older a browser is, the more security flaws will have been found in it. If you haven't kept your patches up-to-date you may be vulnerable.
What About "Cross-Grading"?
Where you change to an entirely new browser. There are many really good Web browsers out there that have features that your standard Web browser might not have. Plus some of the top browsers are under constant attack by hackers and have many security holes. You may be pleasantly surprised at the features you were missing by sticking with your major label Web browser.
Why Not Keep the Old Browser
Sometimes the decision to upgrade is actually a bad idea. If your readers come to your site with primarily older browsers you could be doing them a disservice by upgrading, as you would no longer know what your site looks like to them. Many developers, when they upgrade, keep the old browser versions around for testing purposes. I actually can test my site in Netscape 1.0 if I want to.