Helping people with computers... one answer at a time.
Backing up properly can take up a fair amount of space. Exactly how much space a backup will take depends on several factors.
Which takes more disk space, back-up, or copying files? To date I have only copied files (.doc, .jpg, etc.) but probably need to do a back-up. How much space is required in relation to the amount of space already in use on my hard drive?
Naturally, it depends on how much you're backing up, how you're doing it, and what tools you're using to do it. It even depends on what kind of data you're backing up.
Copying files takes up exactly as much space as the files you're copying, that's easy.
You can often reduce the size of your copied files somewhat by compressing the results. For example instead of copying a set of files, you might create a zip'ed archive of those files and save that in a safe backup location. It'll normally be smaller than the sum of the files that went into it. How much smaller? Well, as we'll see in a moment, that depends.
As you can probably guess, I'm a big believer in performing full backups of some sort. That way you know that everything - whether you thought you might need it or not - is backed up. With the right tools, recovery from a catastrophic failure is a simple restore from that full backup. Everything, Windows, your applications, your settings, and your data can all restored from your most recent full backup.
How much space will that full backup take?
Well, "worst case" is that backup will take exactly as much space as your original files take up. In other words, a full backup is just a special kind of "copy" of all of your original files. Instead of copying just a few files as you're doing now, everything is copied. (It's a special case, and requires some kind of special tool or technique, because certain files which cannot normally be copied while they're in use must also be copied.)
The good news is that most backup programs actually also compress your data as you backup. A good example is my own machine - as I write this my C: drive contains roughly 62 gigabytes of data, but the last full backup of the drive is only 50 gigabytes due primarily to compression.
But of course that's not the whole story.
A periodic full backup is often only part of a complete backup strategy. In my case, in addition to that 50 gigabyte full backup image, there's an another 120 gigabytes of daily incremental backups.
As a result, how much space your backup is going to take will depend in part on exactly what backup strategy you elect to take. A once a month a full backup that gets overwritten each month is going to take up less space but provide fewer recovery options than the same plus a daily incremental backup. It all depends on what you need.
Finally, a word about compression.
In short: compressing data that is already compressed will not save much, if any, space.
For example: if you're backing up your collection of MP3 files, those are already compressed. MP3 is a compressed format, and attempting to compress it again, even as part of a backup, will not make MP3 files much smaller. The same is true for any compressed file format, which includes almost all images, music and video files. If you have lots of those, then expect the backup to be closer to the same size as the original files themselves.
On the other hand, if you're backing up primarily documents, programs and the like, you may see much better compression.
Ultimately my recommendation is simple: invest in good backup software and a large external hard drive (USB or Firewire) that has the capacity to do full backups, perhaps with periodic incrementals, to meet your needs. For example my primary "C:" drive is 70 gigabytes, but my backup drive is 250gig - more than enough to handle the backup strategy I've settled on. In the long run, it really is worth it.