Use versions like /v1/ .
If there's no version... * If there request is plain html then deliver a human readable documentation page (that still has hyperlinks for discoverability. * If the request is asking for whatever your application type is, redirect to the current stable version.
If there's an older version requested: * If it's no big whup, keep the old version usable. Sometimes I do this by just keeping the old version of the resource code around, sometimes by updating it to translate between the old version and the latest stable version. * If you want to kill an old version, think about what appropriate in terms of 300 Multiple Choices, 301 Moved Permanently, or 410 Gone relative to your users.