Physical Risks
Physical danger
Hackers on the internet arn't the only things you have to worry about. There are plenty of enviornmental dangers that you will have to face to keep your computer up and running.
Too much Electricity -surges
Every desktop computer should be, and probably is connected to a surge protector. Surge protectors are appliances that when they have too much voltage go through them will break instead of allowing the voltage spike to ruin more expensive devices.
Surge protectors have several great things going for them. They usually act as a short extension cable, give you about five extra outlets, protect your electronics, Cost 15$ or less and best of all usually come with a several thousand dollars worth of surge insurance just incase they fail to protect.
If a surge hits your computer, then odds are you will have every single component fried (whether it's on or off) so it's best to be on the safe side (no matter how rare surges are.)
Heat
Active computers can generate a lot of heat. As a computer gets hotter it starts to lose its stability, so if you don't like random freezes or unexpected shutdowns then you better make sure your computer can keep itself cool enough.
Keeping your computer cool is simple enough. For most computers you just have to give a little bit of space between the exhaust fans on the back of your computer and the wall, and maybe do a little dusting every now and then and you're probably not going to have any problem with overheating. If you have a high-end machine then you might also want to make sure than no cables are blocking the airflow through the computer (cases usually have something on the front so that fresh cool air has a place to get inside.)
If you followed the previous steps and still suspect that part of your computer is overheating there are several utilities you can use to check on the temperatures inside your computer (most major components have built in thermometers) such as SiSoft. If a component is too hot (they'll all look too hot, check online to see if they actually are) you should be able to get it replaced (if it's under warranty), or find a replacement for the devices cooling system.
Water
Water (well not 100% pure water, you could safely dunk a running computer in that) can short out and fry several parts of your computer. The risk of water is mostly geared towards keyboards and laptops, since the odds of spilling anything into a desktop are pretty low. If you do spill some thing onto your keyboard there is about 30/70 chance of it shorting out or just getting a little sticky. Laptop keyboards generally have less space between the keys, greatly reducing the risk its keyboard breaking.
If water starts to condense inside your computer (not that the average person will have his computer open while it's runnig) I recommend ignoring it. but if you're worried you can always turn off the computer.
Theft
Use some common sense and don't ever leave your laptop out in the open unsupervised, and lock it up when it's in public space. If that's not enough to make you fell safe, there are a few programs that will make tracking down who stole your computer fairly simple once the thief connects it to the internet.
Stolenlaptop.com offers a list of these programs. You can use it to find the right one for your needs.