Today, Google Chrome (the world's second largest browser) got all of these APIs and more (except WebRTC, but it's in the dev build, so it will soon be here too). Chrome even have it's own built-in appstore (Chrome Web Store) where users can install extension/apps, without having to restart their browser.
Another approach to get Spotify to the web is to use Native Client (NaCl) to compile C/C++ code for the web. An example is the game Bastion that was compiled with NaCl to run in Chrome.
This would be the easiest way for the Spotify developers, as they only had to tweak their code very little to make it compile with NaCl.
( Offtopic: I made a chrome extension for Spotify, which convert spotify links to links with mouseover info, for example image of the album, artist name, title of track, popularity. Get it HERE. Thank you :] )
A chrome/firefox/explorer extension that will automatically pause the music on spotify when you are watching a movie.
This is one time I'm all too happy to go back on my words from my previous update.
We're happy to announce that we have a beta web player available to some users. Keep in mind the beta version is still being worked on and will be available in the early part of next year. For now, try it out at play.spotify.com.
Since we're still in testing, that link might not work for everyone at the moment. If you're unlucky enough to not be taking part in the beta please just sit tight and we hope to be able to bring you the Web Player as quickly as possible.
We'll update this thread once the official version is released.