Spotify allows premium users to install the application on as many devices as you like. And up to 3,333 songs can be synced for offline listening on up to three devices at a time.
However, you can only stream music on one device at a time. If you begin playback on another device, the playback on your current device will be paused.
The exception to this is if you pay for a Family plan, which lets you stream from multiple devices at once (http://spotify.com/family).