I have updated my Base Master Pages again, this time changing or adding the DOCTYPE tag in each. Please note that the base master pages include the HTML Transitional DTD that will display your site in quirks mode. Please replace the DTD if you need a more refined presentation mode for your site.
I selected this DTD because it can assist the broadest audience (older browsers, mobile views, newer browsers, etc). If you want to use a standards compliant presentation mode, you can switch the DOCTYPE to:
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
or
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
For more info about DOCTYPEs, check out the info at W3Schools.