Computers do weird things when they get too hot (like die). Some computers are worse than others in terms of how they handle heat. If your laptop suffers from this or you're playing in a really hot climate, consider getting a laptop cooling pad such as this Belkin pad shown on amazon.com.
Vibrations caused by loud music can cause your harddrive to work a lot harder to serve up a stable audio stream. I remember playing a show in Germany on a wooden stage where randomly throughout the set, the floor would vibrate so bad when there was heavy bass, the laptop's disk protection crap would kick in and my audio would drop out. Putting the laptop on a padded surface to absorb some of that vibration did the trick. Additionally there are some PC laptops with software on it by default which shuts down the drive if it senses too much vibration to protect your data. Obviously that's not good in a live performance situation. I recommend using eggcrate padding. It absorbs vibration while still providing an air path under the laptop to keep it cool(er).
No surprise here. Water and computers do not mix. You can consider this risk in two ways:
Weather - Some locations you may play are just inherently humid, like tropical climates or outdoor festivals where it has rained for days. There's not much you can do about this except try to keep your laptop in a dry place (like back stage) until just before you go on to at least minimize the amount of time it is exposed to the elements. Larger, more well funded tours may also offer you the capability to have a dehumidifier with you on back stage to remove any moisture from the air before taking the machine outside.
Direct contact (i.e. whoops, I just spilled my beer on my computer) - Shit happens. From what I've read, the best thing to do is to immediately turn the machine off, disconnect the power and remove the battery. The risk of any long term damage apparently greatly goes down if there is no actual power applied to electronics when it gets wet. Allow the laptop to completely dry before turning it back on to assess the damage. I have seen some people use a hair dryer on their machine to try and quickly dry up any moisture in it. If you do that just make sure you keep the hair dryer on low, keep it moving and don't stop on any specific part, and make SURE you let it all cool down before attempting to turn it back on. There are plastic covers you can get for certain computers to help protect against spills on the keyboard too.