Very underrated subject. If you have Windows Vista or Windows 7, they both have local backup solutions. All you really need is an external hard drive.

Local Backups

Windows 7 Backup: http://windows.microsoft.com/en-US/windows7/products/features/backup-and-restore
Windows Vista Backup: http://windows.microsoft.com/en-US/windows-vista/products/features/security-safety

Here is a link to Lifehacker.com that features third party backup software: http://lifehacker.com/#!5787572/set-up-an-automated-bulletproof-file-back-up-solution

Most "experts" would recommend you have both local and online backups. This really is only if you have data on your computers that you absolutely cannot live without or are like me and this kind of stuff interests you. (adjusts nerd glasses) The easiest solutions to get into would be Cloud aka Internet Backups.

Cloud (aka: on the internet) Backups

Along with local backups, its also good to have cloud (remote) backups. The easiest solution for this is to get a Dropbox account. You get 2GB of storage and syncs a folder in your "My Documents" folder automatically. (http://db.tt/Vov6qZA) Disclaimer: that is a referral link, if you use that link to sign up, I get some extra cloud storage.

Another easy solution that is a little more flexible than Dropbox is Windows Live Mesh 2011. (http://explore.live.com/windows-live-mesh?os=other). Also available through Windows Update (Windows Live Essentials). You get 5GB with this solution and you can sync any folder on your hard drive. (I also have this)

A little more technically advanced solution would be JungleDisk. This service isn't free but is pretty cheap none-the-less. (https://www.jungledisk.com/personal/) This service is $2/month for Simply Backup or $3/month for the Desktop Edition (which comes with some extra features). You get a default 5GB with this level of service and it costs $0.15/month for every gigabyte after that. I use this to backup this forum, the other manvolve network sites and all of their databases.

The Complete Cloud Solution

Mozy
This used to be a complete backup solution with unlimited storage for about $50 a year. While it still is a complete backup solution, it limits you with a few tiered pricing options. (http://mozy.com/home/pricing/)

• 50GB - $5.99/month
• 125GB - $9.99/month

Most people probably barely have 50GB worth of data, let alone 125GB worth, however these are still expensive options if you ask me. I've heard this is a very reliable service since I've never actually used it.

Carbonite
This service is still a complete unlimited backup solution. You can backup your entire computer into the cloud for $54.95. No plans have been made yet, but they might follow suit with Mozy to discontinue the unlimited offer. If you sign up now, though, you would probably be granfathered in. How it works: http://www.carbonite.com/en/online-backup-software/how-it-works

Summary
By far the easiest and most fool-proof solution would be Carbonite. It is highly recommended among those who know about backup solutions. While I have never used it, it seems like the best solution. The easiest point of entry into backup would be Dropbox since its free and also easy. Dropbox is the best choice of you need to sync files between multiple computers or need to share files among a group of individuals.