For those of you who don't need a full-fledged backup solution but are just looking for a simple, easy to use file synchronization program, I highly recommend
FreeFileSync. It probably lacks a lot of the features of the commercial products that others have recommended, but it does file synchronization quite well, and is reasonably fast. It also sports a nice clean and intuitive user interface.
It is free, open source and, perhaps the best part, it's updated very frequently--usually once every week or two, sometimes with only days between updates. And the developer seems to check the
project's forum fairly often if you need help or have feature requests.
And, despite this being my only post here, I am not affiliated with the project in any way other than as an end user.