It is important to follow the correct procedures when you shut down a Linux system. If you fail do so, your filesystems probably will become trashed and the files probably will become scrambled. This is because Linux has a disk cache that won't write things to disk at once, but only at intervals. This greatly improves performance but also means that if you just turn off the power at a whim the cache may hold a lot of data and that what is on the disk may not be a fully working filesystem (because only some things have been written to the disk).
Another reason against just flipping the power switch is that in a multi-tasking system there can be lots of things going on in the background, and shutting the power can be quite disastrous. By using the proper shutdown sequence, you ensure that all background processes can save their data.
The command for properly shutting down a Linux system is shutdown. It is usually used in one of two ways.
If you are running a system where you are the only user, the usual way of using shutdown is to quit all running programs, log out on all virtual consoles, log in as root on one of them (or stay logged in as root if you already are, but you should change to root's home directory or the root directory, to avoid problems with unmounting), then give the command shutdown -h now (substitute now with a plus sign and a number in minutes if you want a delay, though you usually don't on a single user system).
Alternatively, if your system has many users, use the command shutdown -h +time message, where time is the time in minutes until the system is halted, and message is a short explanation of why the system is shutting down.
# shutdown -h +10 'We will install a new disk. System should > be back on-line in three hours.' #
Broadcast message from root (ttyp0) Wed Aug 2 01:03:25 1995... We will install a new disk. System should be back on-line in three hours. The system is going DOWN for system halt in 10 minutes !!
When the real shutting down starts after any delays, all filesystems (except the root one) are unmounted, user processes (if anybody is still logged in) are killed, daemons are shut down, all filesystem are unmounted, and generally everything settles down. When that is done, init prints out a message that you can power down the machine. Then, and only then, should you move your fingers towards the power switch.
Sometimes, although rarely on any good system, it is impossible to shut down properly. For instance, if the kernel panics and crashes and burns and generally misbehaves, it might be completely impossible to give any new commands, hence shutting down properly is somewhat difficult, and just about everything you can do is hope that nothing has been too severely damaged and turn off the power. If the troubles are a bit less severe (say, somebody hit your keyboard with an axe), and the kernel and the update program still run normally, it is probably a good idea to wait a couple of minutes to give update a chance to flush the buffer cache, and only cut the power after that.
Some people like to shut down using the command sync  three times, waiting for the disk I/O to stop, then turn off the power. If there are no running programs, this is about equivalent to using shutdown. However, it does not unmount any filesystems and this can lead to problems with the ext2fs ``clean filesystem'' flag. The triple-sync method is not recommended.
(In case you're wondering: the reason for three syncs is that in the early days of UNIX, when the commands were typed separately, that usually gave sufficient time for most disk I/O to be finished.)
sync flushes the buffer cache.