Helping people with computers... one answer at a time.
External hard drives are a great convenience, but they're often used in different ways. As a result, maintenance needs may also be different.
Should I treat my external drive (used for backups) just like I do my internal drive which is subject to regular maintenance tasks like Disk Cleanup, Defragging and so on?
As with so many things, "it depends".
Whether or not, or how, you need to maintain your external drive depends on exactly how you use it.
Understanding what each of those maintenance tasks really do should help you decide.
You mention that you're using your drive for backups, so this part may not apply to you. But then again, depending on what you mean by "backup", it might.
I don't even have to ask how you use the drive for this one, the test is simple: if your external drive died and was completely unrecoverable, would that be a disaster or an inconvenience? Would you lose things that you cared about?
If it'd be a disaster you know what that means: you should be backing up the contents of your external drive. Perhaps you'd get another external drive to backup to, perhaps you'd backup your external drive to your internal and vice versa (totally valid, as long as the data is in two places on two different hard drives), but you should be doing something.
To be honest, I don't even run this on my primary drive, but then I'm also a little geekier than average and know what to clean up manually and when.
If all you do is run a backup program to your external drive, then the only thing you need to do in terms of cleanup is keep an eye on disk space. When the drive starts to get too full, you'll need to delete something. Exactly what depends on how long you want to keep your backups, and exactly how depends on the backup program you're using. But there's nothing that the disk clean up utility would do that would help.
If you use your external drive for other things disk cleanup may help, but in reality it's still going to be focused on items that more traditionally live on your primary or system hard drive. Even if you're doing things other than backup with your external drive you should probably still just keep an eye on the amount of free space on the drive and take appropriate action if it gets too full.
First, realize that defragmenting a drive is only a performance optimization. In other words the only reason to defragment is to increase (or maintain) the speed of your hard disk. Particularly with an external drive, the USB or Firewire interface will often be the real limiting factor on speed and defragmenting the disk will have little to no impact.
In my opinion defragmenting is really also only called for if the drive is "busy". By that I mean that lots of files are being created, deleted, written to, moved around and so on, every day. That's typically not what happens on a backup drive. They get written to infrequently (when the backups happen) and that's about it.
Fortunately with most defragmenting tools, Windows built-in tools included, you can tell whether or not defragmenting even stands a chance of being helpful by running the analysis that the tools offer. I'll bet that the majority of the time there's simply no need.
Since external hard drives are in their own case and have their own ventilation systems, this one's easy to overlook: it's probably a good idea to vacuum the ventilation holes to suck up any dust or debris that may have accumulated. This doesn't have to happen very often, not even as often as your main system's box. But since you should be giving your PC a quick vacuum every so often, that's a fine time to do the same with your external drive.
Just remember to turn both off when you break out the vacuum.