setup mozy and forget about it
Not a good idea to implement and forget about
any backup solution. Any solution used may run into issues over time and if you are not confirming that the backup is working then you won't know this until the time comes when you need to restore.
To the OP, look at your data and decide (a) how important is it and (b) how important is your access to it. Not all data is likely to have the same ratings in both (a) and (b). Files which have a high "a" rating may need a more comprehensive backup solution to ones which don't. For files which have a high "b" rating then you should consider placing them on some sort of RAID solution, (obviously not RAID0), to maintain access to the files even if a disk fails without having to resort to a restore.
Note though that RAID is not a backup mechanism and any files on a RAID array still need to be backed up.
If you have a small amount of data that you want to backup then use an online service provider but make sure it is working and that you can easily get at your data, (even from another machine), and that it is not corrupt (I've read some horror stories about Amazon S3 based solutions). If you have a large amount of data then you are going to realistically be looking at USB drives which you need to hold offsite ideally. The former should provide you some sort of tool for backing up, the latter you can use whatever copy method seems suitable be that synctoy (or equivalent) or even Windows Explorer drag and drop. But remember to keep it simple and tested.
Personally, in my setup important files are kept on a NAS (configured as RAID1). These are backed up nightly to a linux server at my parents over an encrypted tunnel, (the NAS is mounted onto a linux server which then backs up the relevant files using rsync over an SSH tunnel). I also back this up to local USB disk on a monthly basis.
Less important files sit on a RAID array in a linux server. These are also held on two other machines in the house, (mostly media data, e.g. CD/DVD rips), which it is synced to each time it is updated (synctoy). This server is also backed up to USB disk monthly and this disk kept offsite.