Napster, the formerly infamous peer-to-peer file sharing service now turned legit has just released its first iPhone app to bring its cloud music streaming service to your iDevices.

For those of you who don’t know the new Napster, it’s now a subscription-based music streaming service. After a free 7 days trial period, its $10/month service gives you access to a very large music library that you can listen to as you please. Think of it as an all-you-can-eat iTunes music store. With the difference however that you never really own the music you’re listening to, as it’s streamed to you from the cloud.

The Napster app released today is basically a client for their service that brings it to your iDevice. Interestingly, it partly takes away the need for a continuous Internet connection as the app can cache your playlists for offline playback. Further on, it also packs a recommendation feature that will help you find new songs based on your tastes.

Unfortunately, the service is US only for now and requires you to have a Napster account (you can sign up from a link in the app).

This might become a serious threat to Apple’s own music store if it takes off. Yet, who knows if Apple won’t be coming with something similar of its own very soon, especially after they acquired LaLa, a similar service to Napster last year.

The Napster app is available for free, now on the Apple App Store.

[Thanks to all of you who sent this in!]