Videos
I noticed in the sidebar that it recommends installing extensions for your browser to open most Spotify links in the desktop app. There's actually a much easier (official) way of doing it now.
Go to http://play.spotify.com/settings (the Spotify Web Player settings)
Third from the bottom is "Play open.spotify.com URLs in desktop app". Click the switch beside it to enable the setting.
Done! All open.spotify.com links should now open in the desktop app.
NOTE: it doesn't work for play.spotify.com, which I've noticed pops up in r/music sometimes. In that case, you can replace play.spotify.com with open.spotify.com in the URL, which will redirect to a simple playlist web page, then you can click the play button and it will open in the desktop app. Otherwise, it will still try to launch the playlist in the Spotify Web Player.