Recommendation for back-up

At home, I have an internal hard-drive in my G4 tower that I do a daily back up to with Silverkeeper. This little program is free.

At work, we use a network backup with Retrospect but that's a little overkill for a single user. However, that backup is duplicated to an external firewire Lacie hard drive. 320gb Big Disk Extreme...

Why the Lacie?
Solid case, good reliable experience with Lacie drives, choice of connections i.e. 2 flavours of Firewire & USB 2 if you want it.

Just to expand a little after reading your machine's specs in your signature...

For a cost-effective solution (but not portable):
Purchase another internal SATA hard-drive for your G5 of a similar or larger size than the existing one. Install it (it's a breeze & takes about 5 mins).

Then... use Carbon Copy Cloner to clone your existing hard-drive. This will give you an exact replica of your current installation. You can use this to do scheduled 'clones' or simply backup your home folder on your main drive with Silverkeeper to the Users folder on the backup drive which is what I do...

The advantage of all this is that the backup drive will be fully bootable & if your main drive ever stops working, you'll be able to continue exactly where you left off with a minimum of hassle. Because it's a clone, it will have all of your applications & settings just the way you like it...

What Blue Velvet says is a really good idea. But I'd also recommend that you back up to CD/DVD in addition to a hard drive (internal or external). You will never regret having multiple backups. I have an external HD that I back up to, but I also back up my documents and emails to CD. I keep the disk in a small fire-proof safe. That way, even if the computer burns (with the house/dorm/apt or the power system fries the entire system) I still havent lost much.