What DOCTYPE should be used, for a web application? What are the different DOCTYPES available, and what are they for?
See this W3C page: Recommended list of DTDs
EDIT: As well as this W3C page: Tips for Webmasters :: Doctypes
Also see Section 7.1 and 7.2 of the HTML Spec. as to why. Another very important reason is that using a fully qualified document type declaration (if it is the very first line of the document) gets IE out of "quirks mode" and into a fairly standards-compliant mode with regard to the rendering of block type elements, making it much easier to get your pages to render the same in IE and other browsers.
