To bypass all my school filters, I use OpenSSH and Putty for the client. Has not failed me yet. I have found that using port 443 (SSL) is typically open at most schools.
As for your gaming situation, I use Hamachi (which was recently bought by LogMeIn) to create a P2P VPN, then I will use tightVNC within the encrypted tunnel for remote desktop work.
Below are some links to sites regarding setup of OpenSSH.
Hope that helps.
http://www.buzzsurf.com/surfatwork/#router
http://puremhz.com:8080/showthread.php?t=3424
http://www.hamachi.cc/