I've done some research, and found that on average, 80% of the music I listen to on Spotify was coming from peers rather than from Spotify's servers. If I'm anything like an average user, that means that Spotify may be cutting its bandwith costs by something like 80%. That would be impossible to do as a web app, and web-based competitors face huge streaming costs indeed.
But seriously, I don't think Spotify could be the great app it is if it were a flash app. Can you imagine yourself running a tab in your browser with an app like Spotify inside and your fans running full-speed on?
The web as a platform still has trouble keeping up with capabilities of desktop apps from 10 years ago. But due to having pretty much no reasonable competitor in the deployment market and deployment being so essential to a company's success the web will likely continue to be a dominant platform for startups and should eventually catch up to desktop platforms(probably 5 years or so).
Compute-intensive and graphics-intensive applications
E.g. for a Windows app: reading files, connecting to Outlook, adding things to the registry, Windows Explorer context menu support, draw stuff on the desktop, plugin for Visual Studio, easier task-tray integration, better global shortcut key support, Win32 API trickery if you need to make controls do what they don't currently do.