Amazon dropped the ball. Really their only advantage was No DRM but now that iTunes Plus is standard, that went away fast. Since their launch years ago, Amazon has done next to nothing to improve the user experience.
Microsoft is actually doing some interesting stuff with Zune, but they've really positioned it as a niche product for anti-Apple gearheads, not the mass market.
I think Google is by far the most likely company to launch a serious iTunes competitor. With all the work they've done on Android to compete with the iPhone, a music store/service would be a logical next step.
i've said this before but now it's really starting to become apparent: google wave is the google OS; the webOS that we've been talking about.
Google is working on a music-related service, but I don't think it'll involve streaming or downloads.