We're not sure how long this has been possible, but at launch, Amazon's Cloud Player refused to stream songs from your Cloud Drive in Mobile Safari, with the only alternative being selecting 'Download' instead of play. Now Amazon has quietly flicked the switch that allows Cloud Player to work properly in Mobile Safari, once you get past the "Your browser isn't supported screen," complete with background playback and control, meaning that you can pause the music and skip tracks right from the multitasking bar.
If you haven't tried Amazon's Cloud Player, and you've got an iPhone, iPod touch or iPad, perhaps now's the time to give it a test drive. You get 5 GB of free storage up front, and you can upload and stream any tracks you already have with it. Anything purchased from the Amazon MP3 store can be automatically added to your Cloud Drive without counting against your storage quota. What's more, Amazon will give you an extra 15 GB of free storage when you purchase at least one MP3 album, bringing your storage limit up to 20 GB.
While any web app implementation isn't going to be as good as a really great native app, using the Cloud Player in Mobile Safari with background playback and control isn't a bad option at all -- plus it works outside the US, too.