I found several tutorials about how to get Cisco Anyconnect VPN software running for ubuntu 64 bit. However, I'm a very minimalistic person and I knew that the instructions I'd seen Here where overboard. I couldn't figure out why I actually needed to install firefox 32 bit if I only needed some libs from the 32bit version of firefox.
I tried installing the libraries (ia32libs and lib32nssmdns) and then symlinking to them from /opt/cisco/vpn/lib
however, I still received the "Certificate could not be verified" error message.
I found a pdf from the Berkley website which had the solution, which was several less steps and didn't involve actually installing a 32 bit browser (that you don't need).
Here are the steps:

Perform a manual installation by whatever means you have available (if you have the installer use, that, or if you can get to the anyconnect website, you should be able to install from there.) Once you have the installer, run the following:

  cd ciscovpn && sudo ./vpn_install.sh

(Actually, I found that if I login to my vpn through my webbrowser, it does download and install, it just doesn't connect because of the certificate error, so I didnt have to do the above step). Here is a recent version if you can't get it elsewhere.

Note that with the version I have posted here I was able to use without any of the below instructions on ubuntu 10.04. Your mileage may vary, but for me it worked out of the box (I am using the Sun jre though so not sure if it works with openjdk).

If you have any problems about a Security error as described previously, do the following:

1. Install ia32­libs and lib32nss­mdns:
   

      sudo aptitude install ia32-libs lib32nss-mdns 
   

2. Add several symlinks in /usr/local/firefox (create this directory if needed):
   

      cd /usr/local/firefox 
      sudo ln -s /usr/lib32/libnspr4.so 
      sudo ln -s /usr/lib32/libnss3.so 
      sudo ln -s /usr/lib32/libplc4.so 
      sudo ln -s /usr/lib32/libsmime3.so 
      sudo ln -s /usr/lib32/nss/libsoftokn3.so 
   

Thats it, Now you can connect.
Hope this saves someone from having to download firefox and complete other unnecessary steps.