With OS X Mountain Lion (and later versions), you can enable system-wide audio streaming to any AirPlay speaker, allowing you to use services like Spotify, YouTube and others in conjunction with AirPlay on your Mac.
To enable this, open System Preferences > Sound and choose the "Output" tab at the top. In the centre of the window, you will see a list showing the available AirPlay speakers on your network. Select one, and all system audio will be redirected to the speaker. (Please note that playback to multiple speakers is still only supported by iTunes).
Tip: To quickly enable transfer of audio via AirPlay to your speaker, hold the option key (the one that says "alt") on your keyboard, while clicking the sound icon in the menu bar.
Note: Sometimes, you might experience a latency issue when watching videos this way, where the video and the corresponding audio are out of sync. This problem is dependent on the video player. Apple's built-in media applications, such as iTunes and QuickTime Player, take the latency into account and display the video accordingly (without sync issue). However, if you use VLC Player (or any other 3rd party video player), the video and the audio will be out of sync.
On the web, videos displayed using HTML5 will work just fine, while Flash videos will cause problems.
On a PC, you are not limited to only using AirPlay with iTunes. With Airfoil from Roque Amoeba, you can "grab" the audio from any application in your system and forward it to any AirPlay speaker on your network.
When watching movies on your computer you should use the Airfoil Video Player (included in the license for Airfoil). This ensures that local video and remote audio always stays in sync. The player supports many video formats, including Flash and Silverlight web video, as well as basic DVD playback.
Airfoil is a third party application, available for both Mac and PC here.