On Ubuntu 11.10, I turned on the 'Desktop Sharing' application that comes with the OS and found that these ports are opened on my computer:

5800/tcp open  vnc-http

5900/tcp open  vnc

They seem to be just the VNC ports.

If you want to verify this for yourself, download this tool from the repository called nmap:

sudo apt-get install nmap

When you install that and have the 'Desktop Sharing' on, run this command in your terminal:

sudo nmap localhost

By default, this will show you all the TCP based ports that are opened. If you don't see any ports open, you might want to look at your local firewall by doing the following command:

sudo iptables -L --line-numbers

This will only list what rules are currently being used on your system.

I hope this gets you on the right track.