The terms VPN (Virtual Private Network) and VNC (Virtual Network Computing) are usually associated with businesses and the act of working from home. However, there are some free (and not free) tools that can be used to extend these concepts to home use.
VPN's are networks that allow computers from different locations to act as if they are all on the same network. Most home computers aren't directly accessible from the internet. A home connection usually has a single IP address which is provided by the ISP and which often changes. You can have multiple computers all sharing an IP address by using a router, which creates a home network and acts a shield against anyone trying to gain access from the outside. VPN's create a link between different networks so that computers can be accessed directly.
A widely used VPN tool is Hamachi. Hamachi is a free program that allows for the creation of small VPN's that can be managed via the internet. Once installed it appears to the computer like a network adapter and includes a utility that lets you see which other computers are online. In Windows, these other computers will appear show up as being part of your Network in Windows Explorer and any shared folders can be accessed.
Using a VPN like Hamachi allows you to share files and folders with friends and family. For example, you can create a shared folder for holiday photos that your family can access and add to. This is particularly useful for things like videos which can be too large to share via email. What's nice about Hamachi is that it works in the background and doesn't require much technical ability to take advantage of.
While not exactly a VPN, Dropbox can also be used to similar effect. Dropbox allows its users to share folders and can be a good choice when you want to distribute files to several people and avoid a bottleneck from having them all download from your computer. Dropbox has a limited amount of space so while its good for getting files distributed to lots of people, as a longer term archive a shared folder is better.
Anyone who has ever tried walking a relative through computer problems over the phone knows how frustrating the process can be. With a VPN like Hamachi in place this aggravation can be overcome through the use of a free VNC client. A VNC application lets one computer take over the other, you can see the screen and use your keyboard and mouse to control the other computer. While there are fancier and more expensive options that do away with needing a VPN, free and easy is hard to beat. I've used TightVNC and haven't had any problems with it outside of occasional disconnects. There are plenty of other options for VNC software including LogMeIn Free which can be used from the same interface as Hamachi and LogMeIn Ignition which can be used from a smartphone.