Trying to find out which browsers support what audio features I found this site: http://caniuse.com/audio
It links to a sound file-format test, where I see Firefox plays only ogg and wav. That made me wonder if one could do mp3 decoding on the browser. It's possible: http://labs.official.fm/codecs/ but it sounds totally broken on Firefox on my Ubuntu.
The playback problems with the JS decoder are due to bugs in some versions of Firefox for Linux. Those have been recently fixed (as of 19.02a as far as I can tell). See: https://github.com/ofmlabs/aurora.js/issues/13
According to hamoid's link my browser has had HTML5 Audio support for almost three years. Yet when I enable plugin on demand, soundcloud (old or new) doesn't work and I have to enable flash. That's Opera. Firefox doesn't work either as was already mentioned.
Every html5 audio test I've found worked just fine. Except for Apple's, because it, similary to soundcloud, sniffs user-agent to serve different version of a site.
Ah, that would make more sense, thanks for pointing that out. Although it's sad that "we" went for expensive Mp3 again when we had a chance to change it. And by "we" I mean chrome. Firefox held a strong stance for quite some time, but had to cave in eventually.
In addition to the HTML5 audio, there are many apps that consume the SoundCloud API. Once I find what I like, I play it with soundCLI [1], but there are many desktop and mobile apps that work outside of SoundCloud's website [2].
Also, you can Chrome to Phone a SoundCloud URL from your desktop and if you have an Android app that reacts to those URLs it will offer to open it.