We found it practical and useful to put the version in the URL. It makes it easy to tell what you're using at a glance. We do alias /foo to /foo/(latest versions) for ease of use, shorter / cleaner URLs, etc, as the accepted answer suggests.
Keeping backwards compatibility forever is often cost-prohibitive and/or very difficult. We prefer to give advanced notice of deprecation, redirects like suggested here, docs, and other mechanisms.
