Pretty much every music streaming service I know of. There were a few that used HTML5, but all of them shut down (most recently rdio).
For Spotify, there's a years old request on the forums [0] their support keeps linking people to, but it doesn't seem like they're doing anything about it.
Deezer uses Flash for "security reasons" [1] and they don't plan to use HTML5.
Someone mentioned Google Play might work, but I haven't tried that yet.
Thanks for the tip...apparently it doesn't work on Firefox, or doesn't work on Linux, or something. I found the switch to enable it, but it's grayed out.
I was painfully annoyed when Songza shut down and redirected to Google Play Music. Songza worked happily without Flash, but Play Music requires it (so far). Also, Play Music has more intrusive ads than Songza.