Option 1: HTML 4.01 Transitional (full version)
<!doctype HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
the above doctype is the best choice when:
You are building new pages and you are unsure what doctype to choose
You are using a tables-based layout or are placing images in tables
You want to use older (presentational) markup
You want to open links in new windows
the "full" version of the HTML 4.01 Transitional doctype is the best all-rounder - it triggers Standards Compliance Mode in modern browsers ("Almost Standards Mode" in Firefox), it contains all the necessary elements and attributes including deprecated (older) features. If at all unsure, choose this doctype!
Option 2: HTML 4.01 Transitional ("half" version)
<!doctype HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
This doctype is different from the "full" version above in that the URL for the DTD is missing. This means that the page will be rendered in Quirks Mode in modern browsers. Quirks Mode means that the browser handles the markup in a compatible way with older browsers such as IE5 or Netscape 4.
the "half" doctype is the best choice when:
You have an existing tables-based layout that you are trying to validate
Using a newer doctype breaks the page design, and you do not want to rewrite the page
Your tables-based layout needs to work in very old browsers (IE3/5, Netscape 3/4...)
You should never use the "half" doctype when using CSS for layout, as the browser will not handle the the layout according to the established specifications. This will cause a lot of cross-browser headaches. Using the wrong doctype is an extremely common reason why CSS-positioned layouts fail. the "half" doctype is good for converting older pages when you don't want to recreate the whole thing - but for new pages, it is best to use the "full" version or HTML 4.01 Strict.
If you have older pages but you don't want to clean them up or make them pass validation, then there is no advantage in adding any doctype at all. When a browser encounters a page without a doctype, it automatically selects Quirks Mode and handles the page like an older browser. So if you have legacy pages without a doctype, don't worry about it until you want to rework those pages - they will continue to function as before for the foreseeable future!