Is there a way in jsBin or jsFiddle to get a link to the page you created as is, without being embed inside a frame? If not, is there such service (something that would let me quickly create an HTML page and see it live with one click)?
UPDATE: Since Feb-2017(?) it seems this method no longer appears to work unfortunately.
You seem to be able to do this in jsFiddle by first getting the "Share full screen result" URL (from the Share menu) and then view the source of the full screen result to get the URL of the iframe used to display the result.
For example, the "full screen result" URL, which still shows a minimal toolbar at the top:
From this, you can see the URL of the embedded iframe, which is: