Do users know that they're not using the current version of their browser? While many browsers will check for updated versions (Firefox, for example), some do not.
Anywho, I've decided, looking at the numbers, that I would start adding a check on my sites to alert users if there browser is out of date, and tell them where they can get an updated version.
Note that I refer to the desktop version of these browsers, and mention only the major browsers. From personal experience, I highly recommend Opera's mobile browser(s).
Internet Explorer
Update 12/21/2008: After looking through my logs, I found a couple of instances where the MSIE 6 and MSIE 7 instances show up in the user-agent, as well as MSIE 6 and 8. This seems to be with users who have installed standalone versions of Internet Explorer. If you're using a newer version of IE, but are seeing a message about using an older version, that may be the issue. See this site for more information.
Firefox
Safari
Chrome
Opera
Other browsers
Netscape
For quite a while Netscape (Navigator) was an extremely popular browser. However, it is no longer actively supported.
If you continue to use Netscape most people will recommend that you upgrade to Firefox.