first, i should note that there are tons of things like that which don't require flash. shoutcast.com is one, which just indexes many publically-available streams.
if you want an up-to-date flash, you can use google's pepper flash + the pepper plugin api adapter called "fresh player plugin" (on github or maybe your distro's repos)
grooveshark was also html5-friendly and had tons of good stuff on it. rip :(
then there's mozilla's js-made flash replacement "shumway", which might work for simple streaming flash
strangely, radiotunes.com/apps indicates they have some regular audio stream that should work for winamp or vlc, which could work in the browser, too, but they don't link to any. but i'm not logged in.