A web site testing depends on the type of the Web site.A web
site can be any one of B2B,B2C or a simple Static site.

For testing of a website which has all static& dynamic pages, 

Major scenarios include following:

1)Content check
2)Load& Performance of the website ( Page Load,Response
time,Error Handling during Page Load)
3)Hyper links in each page
4)GUI Testing
5)Platform/Web browser compatibility
6)Third Party Plug in Support
7)Embedded Scripts  
8)Default settings/ configuration tests
9)Security certificate supports
10)Authorization & Authentication features during the
transactions from the website.

Any many more depending on the type of the Web Site.
 

1.Functionality Testing :
      Check the links , Forms , Cookies ,CSS,DB
2.Compatibility testing: 
      Browser , OS Compactability.   
3.Usability testing:
4.Interface Testing:
      The main interfaces are:
      Web server and application server interface
      Application server and Database server interface.
5. Security Testing 
6. Performance testing :
      Web application should sustain to heavy load. Web  
performance testing should include:
Web Load Testing
Web Stress Testing