Anyone recommend a program to backup files?
For file-based backup, my current favorite tool is CrashPlan.
http://www.crashplan.com/Works on Windows, Mac, and Linux and is free for local or peer-to-peer backup. Online subscription is pretty reasonable for unlimited data.
For smaller amounts of data,
Dropbox is a decent backup solution as well, but it's really more suited for file sync than backup, IMHO.
For whole-system image-based backup, I use
Acronis True Image. My only complaint about it is that their new releases tend to be somewhat buggy. Best to wait a while before upgrading each version. Other than that, I haven't had any problems with it and it has saved my bacon a number of times.
A similar product that is also good is
Macrium Reflect. Not quite as full-featured as Acronis, but seems to work fine in my testing.
For a super lightweight solution, another nice imaging tool is
Drive Snapshot. The cool thing about it is that it is only like a 500k executable that requires no install. (Unless you want the Windows file associations to browse its backup archives in Windows Explorer.) The only real drawback is that it doesn't have any built-in scheduling capabilities for automatic backup, but if you're handy with batch files / powershell / etc, that's pretty trivial to do on your own.
And of course if you're using Windows 7 (Professional or greater, I think...?) full system image backup capability is
included in the OS.