MODS PLEASE NOTE: My descriptions of specific programs are purposefully vague. Remove any links that break the rules... I don't think there are any though.
You can't change the ports programs use because the ports used are controled by the REMOTE computers (ie over the internet).
I've actually tackled this problem myself over a period of four years, here are the options I've considered, ending with the best one available IMO.
Find free dialup in your area
PROS: Can't be caught, unless you've being investigated by the police or something.
CONS: Slow and low caps, unless you wanna pay for it. NetZero had something like 10mb/mo free. There was this one completely free offering in my area but you needed caller ID.
Google and find a suitable proxy to use.
PROS: Endless supply, even if they block some (they probably already do). Can be used to update torrent trackers, if specific trackers are blocked. HTTPS proxies will be encrypted.
CONS: Everyone and their mother knows about them and will be using them. Sloooow.
Leech off of a friend's VPN
PROS: You can play games with friends over the VPN!... Well ok it sucks especially if you have to use TCP to connect to the VPN. Traffic is usually encrypted. You trust the person running the VPN.
CONS: You have to find someone with a VPN and convince them to let you leech off their bandwidth, both up and down.
Set up your own proxy on a machine outside campus
PROS: Noone else is using the proxy so it's nice and fast, you can set up encryption, etc.
CONS: If you have ready access to such a machine you can probably do everything you wanted to do directly from there anyways.
Find a more thorough proxying service such as this one, which I used for awhile until it was blocked
PROS: If you can find one that offers free connections, great. This specific one has multiple servers to connect to and uses ports that IT must keep open (HTTP[S]). Plus all traffic is encrypted.
CONS: That specific service (and prolly others) has a real tight bandwidth cap unless you pay up.
Buy your own broadband connection
PROS: Um, everything?
CONS: They're probably not going to let you add a cable line to your dorm. So it's not happening. Plus it costs money.
Use onion routing. This is my method of choice.
PROS: Encrypted, uses standard HTTP[S] ports, the servers you can connect to dynamically change all the time, no speed limits, untraceable.
CONS: It is possible to block by blocking the dictionary servers used to get lists of onion routing servers. This is how ITS blocked me from using it. But it took them from 1-2 years or something.
Once you have a method, you probably have a proxy server you need to connect your programs through. Many programs such as Steam don't support them. I used
http://www.proxifier.com/ to work around this (a clever computer savvy individual can easily extend their meager trial period if he really wants to).
