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Without open standards, the web would not exist. Using a browser with good support for web standards will improve your surfing experience on standards compliant sites and pages. Here's an incomplete list of some popular browsers.

Graphical Browsers with pretty good support for core Web Standards

Recent versions of:

Mozilla and browsers based on it, such as Netscape Navigator.
Opera is great and constantly improving.
Browsers based on Mozillas layout engine are probably pretty good. Konqueror and Safari are getting better as well.

Graphical Browsers with insufficient support for Web Standards

MS Internet Explorer (version 6 and older) does not support XHTML, and its support for CSS and PNG is insufficient.
Old browsers such as Netscape Navigator 4.