It looks like an offline mode for the desktop Spotify application is in the works. The presence of such a feature has been long-requested by users, but appears to be finally on the cards due to wording in the T&Cs of the mobile app.
Point number 6, under "use of cached content", says "As a subscriber to the Premium Service, you are permitted to store such cached content on up to three (3) personal computers". It looks, therefore, like the offline mode for the Spotify desktop app will only be available to Premium subscribers.
Spotify's mobile application for Android and the iPhone finally went live this morning. We've enquired with the company about how many new Premium accounts it's seeing registered as a result, and will let you know if we hear anything back.