MSDN provides an excellent overview at http://msdn.microsoft.com/en-us/library/bb630354.aspx .
In a situation where no other explanation for slowdowns can be found or when using SQL Server on a server that also has other duties they can be very useful for troubleshooting slowdowns. Generally when using SQL Server on a dedicated machine they are more likely to clutter the display than provide useful information.
answered Oct 18 '09 at 01:42 PM
If you'd like to learn all about Extended Events I suggest reading Jonathan Kehayias' whitepaper on the matter:
Jonathan has also developed an application to help you use and view the extended events information called Extended Events Manager. The application is free and available at Codeplex: http://extendedeventmanager.codeplex.com/
answered Oct 19 '09 at 08:32 AM