I modified the master page of a site and I would like to make all new sites that get created to use this master page by default. Is there a way to modify the built in site templates to use this master page by default using SharePoint 2010?
What you suggest is actually going to break your warranty with Microsoft but there is a safe way of doing it.
You can use an event receiver for Site Provisioned / feature stapling, and set the master page in there for the new site.
Previous answer that should give you what you need to know: Apply custom master for new site collection and sites under