If you go to "My computer", you can see how many gigabytes of data you're currently using. Of course, not all that data is necessary to backup (for instance, Windows itself takes up a few GBs). However, you should at least be able to account for most of the gigabytes there.
If you right click any folder and go to properties, you can see how many gigabytes of data it's using. If you examine the folder sizes of all the folders in C:/, their sum should match the amount of space you're using on the hard drive itself (mathematically, this must be true). You can get some idea of where the data is, and how to get it.
In general, I'd start by going to "My computer", and then going to your hard drive (or hard drives), and looking through the folders and backing up anything that you might need in the future.
The program files folder (C:/program files) usually contains the data for programs that you installed. Although you'll probably have to reinstall any programs when you reformat, you might want to save any data that you've stored for the program. For instance, if you play any computer games, you might want to backup your save files, replays, screenshots, etc.
Also, remember to back up any files you've placed on your desktop, as well as files in the "Documents and Setttings" folder.
You can also do a file search -- under advanced settings, you can specify dates and times. Search for files that were created and/or modified in the past 2 weeks or so, and you might get an idea of where files are being stored. Of course, you'll have to filter through a bunch of garbage files that are automatically generated by various programs (for example, "temporary internet files" and stuff like that).
Once you get a new hard drive, one approach I'd recommend is keeping all the files that you need in a single folder. For example, put all important documents (documents, videos, save files, whatever) in, say, "C:/my files" -- this way, in the future, if you ever need to backup files again, you'll know that you need only backup C:/my files, and all the other stuff can be thrown out.