Remotely Access Your PCs Over the Network or Internet
Remote controlling a PC on your own network
There are a variety of free utilities that allow you to remotely control PCs on your network. This can be useful for performing tasks on multiple PCs on your home network, or having remote access to any PC in your place of work. All you need to set it up is an account with administrative privileges on the PCs you will need access to.
TightVNC and UltraVNC are two common options. TightVNC is pretty basic (but very reliable,) while UltraVNC has some extra features - file transfers and chat, for example. I've also had better luck using UltraVNC for controlling Vista machines.
Both utilities work the same. A VNC server application is installed on the PC to be controlled. As long as that application is running, any PC that can see that PC on the network will be able ot access it with a VNC viewer. Both the server and viewer are installed with the same installer package. When installing the VNC server, there is a checkbox that will register a VNC service. I recommend checking this box, as it will make sure that the VNC server is running every time the PC is powered on or restarted. Additionally, a password can be set on the server application to make sure unauthorized personnel can't remote control the PC.
After VNC is installed on the PCs you wish to control as well as your own computer, simply launch the VNC Viewer application. It will prompt you for the IP address of the PC to control. After putting in the address, the viewer will check to see if the target PC has a VNC server running. If so, it will ask for the password you set up earlier. Input the password and you will be able to control the remote PC from your own computer.
Controlling a PC over the Internet
While controlling PCs on your network is useful in some situations (or for us IT folk at work,) controlling your PC from the Internet has more practical applications for most people. You can use similar utilities to control your home PC from anywhere you have an Internet connection - or to remote on to a friend or family member's PC.
Logmein is my favorite solution for accessing my own home PC. They offer a free service that allows me to connect to my PC from anywhere - I just have to log onto their website, select my computer, and then log in to my PC. It's secure and works well. They have paid accounts as well that have additional features, but the free account will give you all you need to log in remotely and control your PC.
Much like VNC, there is a server application that needs to be installed on your PC. When you open an account with Logmein, you can select to add a PC to your account. This will allow you to install the necessary software on the PC you're currently working at. It's a fairly small download and the installation is quite simple. Once the application is installed (and your account is verified) you will be able to control your PC from anywhere you have an Internet connection.
Accessing a friend's PC over the Internet
Being in IT, I'm always on-call for any computer issues my friends or family may encounter. Thankfully there are solutions that will allow you to access a friend's PC without having previously installed any software on their PC. TeamViewer is the quickest and easiest I've come across. It's free for personal use (it can be purchased for business use.)
The main difference between TeamViewer and VNC or Logmein is that a server application isn't installed on your friend's PC before you access it. Instead, you both download and run the program from TeamViewer's website. When the program opens, it simply shows you an automatically-generated ID and password, and gives you the option to input a friend's ID to gain access to their system. So your friend will provide you with the ID and password displayed on his PC, and you will use that information to connect to his PC.
This has been extremely helpful in fixing computer problems for friends and family from across town or even across the country. It's also very user-friendly, so guiding a computer-illiterate family member through the process is (relatively) painless.