Such browsers include Internet Explorer 6 and 7, Safari 3 and Firefox 3.5 (or lower).
If you choose to not upgrade (or cannot), Google says unfortunately:
In these older browsers you may have trouble using certain features in Gmail, Google Calendar, Google Talk, Google Docs and Google Sites, and eventually these apps may stop working entirely.
Figures from StatCounter and NetApplications seem to imply that about 17 percent of the world will need to upgrade their browsers, mainly thanks to a huge number of IE6 users in China (over 25 percent).
Venkat Panchapakesan, VP of engineering at Google, says the move is necessary for the future:
These new browsers are more than just a modern convenience, they are a necessity for what the future holds. For web applications to spring even farther ahead of traditional software, our teams need to make use of new capabilities available in modern browsers.