This application will dump all your contacts in CSV format to a text file called 'Contacts.txt' on the root of your SD card. If you can't open the application for some reason (broken touch screen etc..) then reboot your phone and it will launch automatically.
How can you install this without your touch screen? Easy, go to http://play.google.com/ and search for 'Contacts Dump'. You can install it remotely from there, reboot the phone and the contacts will save to the root of your memory card.