Dangers
Steam tunneling carries many risks. It's not a game; like any other potentially dangerous situation, you must be aware of the risks and be prepared to deal with them. Here are some of the perils that may await you if you choose to explore the steam tunnels.
Capture
This is probably the most probable danger that you are likely to face. It's illegal to enter the steam tunnels, a Class 1 misdemeanor in Virginia, which means you can be fined up to $2500 or even face up to 12 months in jail.
It's also against university policy, although the tunnels are not mentioned specifically. If caught, you could be warned, suspended, or even expelled.
The Virginia Tech Police department will follow you into the tunnels if they see you entering them. Even if they don't, someone could call in a report and they could be waiting for you when you leave.
Aside from the risk of someone seeing you, there's also an additional risk posed by the many security cameras that blanket the public areas of campus.
Heat exhaustion or stroke
When you are in a small tunnel with a huge steam pipe running through it, it's pretty obvious that the tunnel is going to get hot. The steam running through the pipes is at least 100 degrees Celsius (that's 212 for you Fahrenheit folks), which means that the tunnels can get quite toasty at points, especially in places where the insulation is not as good.
This heat can be deadly if you're not careful. You should know the signs of heat exhaustion and if you experience any of them, you should get out of the tunnels as soon as possible. Heat exhaustion can and will lead to heat stroke if you are not careful.
To help prevent heat exhaustion, make sure you stay hydrated. Bring water or some other drink down with you and make sure to actually drink it; it's not going to do you any good if you just carry it with you the whole time. Also, don't try to wear a heavy jacket in the tunnels; it's never cold down there, so all it's going to do is make you hot.
Burns
It's pretty obvious that pipes carrying hot steam throughout the campus will get quite hot. If you touch them, you are probably going to regret it. So don't touch the pipes, ever. Also be careful of ladders and other metal objects that can get hot; I would recommend wearing gloves if you must make use of them.
You can also get burned if a steam pipe bursts. Unlike your standard superficial burn, if a steam pipe bursts, you will be in a lot of trouble. Steam condensing on your skin is a very bad thing, but if steam gets into your lungs, you'll be in more trouble. This is how most people die in steam tunnel accidents; inhalation burns carry a much higher risk of death than surface burns. If a steam pipe bursts, get out of the tunnels immediately; the consequences you may face for going in the tunnels are not worth dying over.
Electrocution
Many of the steam tunnels carry power lines through the tunnels. Don't touch with these or mess with them. Many of them are insulated, but you may come across a few that aren't. As long as you don't mess with them, they don't really pose a danger to you.
Asbestos
Many of the steam tunnels and crawl spaces around Tech were insulated with asbestos because of its desirable properties as an insulator. Although Virginia Tech received $350,000 in funding for asbestos removal in 1997, some sections of tunnel and crawl spaces still have asbestos insulation. The pipes that have had their asbestos insulation replaced have a nice "Asbestos Free" sticker on them.
Although it was not known at the time asbestos was originally installed, asbestos can cause all sorts of lung problems. If you're in an area where you think there might be asbestos, you might want to use a respirator. It is only airborne asbestos that can cause problems, however, so intact asbestos does not really pose a threat.
Death
Steam tunnels are not safe places; there are large drops and it's very easy to injure yourself if you're not careful. This applies to other forms of urban exploration as well; in 2011, a UVA student tragically fell to his death while exploring the roof of the locked physics building. His death was tragic, and it would really pain me to hear about this happening here, so do not let this happen to you. Do not let your guard down; be careful where you step, do not make poor decisions about when to go exploring, and always be aware of your surroundings.
More
Virginia Tech's Department of Environmental, Health, and Safety Services has put together a nice guide on confined space safety. The information applies to more than just steam tunnels, but much of the information covered is still relevant. I'd recommend that you check it out if you plan on entering any confined spaces, such as steam tunnels.