Napster goes to iPhone, iPad. It’s about time.

After neglecting the “apps” scene for a while, Napster has finally launched an official app for Apple’s iOS operating system, giving users a well-known alternative to the device’s concentrated connection to iTunes.

Napster, completely divorced from its illegal peer-to-peer sharing roots, lets users stream unlimited music for a $10 monthly fee. The company tried for a while to sell its own dedicated MP3 players linked to user accounts, but that venture never really worked out.

Instead of developing dedicated mobile apps, Napster had until now tried a different strategy. It set up a catch-all mobile website for every smartphone user to access. But that site didn’t give access to streaming music, only offering MP3 downloads that would be delivered directly to the phone’s hard drive. Subscribers to Napster get a limited number of downloads every month.

Today, Napster has officially launched the iPhone app, which not only gives users access to those downloads, but to the more than 8 million streaming songs available as well. It is a free download but of course requires the $10 monthly fee to get any use out of.

Napster also last month released an app for Internet-connected Samsung TVs, allowing users to stream their music directly to the silver screen. There’s no word yet on an Android app or apps for other platforms, but clearly Napster is expanding in that way so it wouldn’t be a surprise to see more Napster apps popping up soon.