Upgrading to OS X 10.6 Snow Leopard makes Juniper Network Connect fail to connect.  I looked through the logs found two things it was complaining about in the "reason=" portion of the dump.  If this doesn't work for any reason, I suggest taking a look at the logs offered to see if that tag has any useful hints.

*** I don't have the foggiest idea how relaxing the permissions on the product directory impacts security | Use this tip at your own risk ***

Here is what I used:

sudo chmod 755 /usr/local/juniper/nc/6.3.0 (This is where the workspace file is stored)

sudo mkdir /Applications/Network\ Connect.app/Contents/Frameworks