Do you recommend from every web site created in Visual Studio, that you should create a Base page that serves as the parent class?
What are the exact benefits/drawbacks?
Check out masterpages this is their primary purpose.
Here's a link: http://msdn.microsoft.com/en-us/library/wtxbf3hh.aspx
This will serve as the template for your site. You would add a content section that would make up the body of your site. You can reference the master page is your subpages to have a consistent layout, menu, etc. for you site.
Also, like the others have noted. If you are running any commond code, just create a class a reference it from wherever you need it.