Bypass VPN for certain apps
Solution 1:
The cisco VPN software supports a "split" tunnel right out of the box. The split tunnel will allow you to keep your internet traffic separate from the VPN traffic. This is exactly what you want to do and should get your spotify program working.
Open up your vpn connection and select the modify option. Once in the modify dialog box click on the second tab. At the top of the screen there is a check box "enable transparent tunneling" Check this box and try it again.
Solution 2:
Latest versions of Cisco VPN Client don't allow you to override the routing if your network admin has disabled local lan access.
Even logging as admin on your local machine and modifying the routing table will not change anything as the VPN Client still blocks it.
Solution 3:
Can you change your default gateway so it uses your internet connection instead of the VPN? This will mean that only things not on the general internet (such as your intranet and fileshare) go over the VPN.
Alternatively, you should be able to setup a static route so that connections to 10...* (i.e. your companies VPN range) go over the VPN and everything else goes to your internet connection. This setup will differ depending on your OS.
Of course, if your company is using "public IP space" (i.e. outside the 10.* and 192.168.* ranges) then it's going to start getting very tricky.
Solution 4:
If you go to the Cisco VPN client preferences. Uncheck "Enable local LAN access (if configured". For myself, I am using a remote desktop connection to a remote location and my local browser resolves to my local IP.