I'll preface this with a note that my experiences are from the Coast Guard Academy, so things may very well be different at the Air Force Academy, however policies typically fall along the same restrictions.
You have no expectation of privacy while on the network. This means if your computer is plugged into the provided internet connection, your computer may/will me monitored.
At CGA you could not connect with a wireless. You cannot have file sharing software, visit hate group sites, or look at objectionable material, yes including pornography. You would not have iTunes connected in "sharing" mode, however you could have in on your personnal computer. There are limits to email sizes.
As a 4/c cadet, no AIM, after that, yes, but it does eat up a lot of study time.
No streaming video or audio.
Most of these rules are to keep the network safe and the poor T-1 line running (it can only take so much).
CGA was a .edu, so there were LESS restrictions than the fleet, .edu allows for some educational packages to be loaded, while .mil has more restrictions and is on a different network entirely.
What is nice, is the govt. can provide you with free anti-virus software, with the assumption that some of your work will be brough home too.
In the fleet there are restrictions on what can be played, configurations, and what you can connect (it is a govt. line).
The Coast Guard Academy also had a program running that would monitor your bandwidth usage, go over and you get called out, if you are #1 you get some serious demerits. No one complained, those bandwidth users were killing my internet speed.
Assume you are being monitored at all times, you probably are.