It seems that the keyboard shortcuts for the Spotify web player are different based on OS and browser!!! And it looks like they tend to change a bit over time!! Thank you Spotify.
These work on OSX with Chrome (I am on a danish keyboard, not sure if this have anything to say)
Space - Play/Pause
Shift+Right arrow - Next track
Shift+Left arrow - Previous track
Shift+Ctrl+Right arrow - Forward in track approx. 15 sec
Shift+Ctrl+Right arrow - Backwards in track approx. 15 sec
Ctrl+Alt+s - Open search
Ctrl+Alt+Up arrow - Increase volume (not above system volume)
Ctrl+Alt+Down arrow - Decrease volume
Any I missed??