Leo Notenboom is the man behind Ask-Leo.com. I've been reading his site/newsletter for a long time and highly recommend it.
Recently, Leo took a 3 week trip halfway around the world and wrote an interesting article about how he handled backups while away from home.
Everyone has different circumstances when it comes to backing up their computer and data, so I am not suggesting copying Leos specific solutions. But copying his approach would serve you well. More specifically:
Have multiple copies of important data at all times.
In the article, Leo frequently refers to two copies, yet he often has three. Certainly, any important file needs to be backed up both locally and off-site and Leo's solution for this, while on the road without reliable Internet access, was interesting indeed.
When possible, avoid having all copies of the data in the same place.
In an approach that would make sense for many, Leo travels with a laptop and a small external hard drive (one based on a 2.5 inch hard drive). When out and about during the day, with the laptop back in the hotel, the hard drive travels with him. At the airport, if the laptop is in carry-on luggage, the hard drive gets checked.
As it worked out, I read Leo's article in an airport while leaving on a trip. Like Leo I travel with two copies of my important files, one copy on a laptop and one on a USB flash drive.
I've done this for a long time, but haven't been particularly diligent about keeping the flash drive with me when the laptop is left behind. Got to do better at that.
Decide what data you can lose and what data you can't.
Perhaps the hardest part of backing up a computer and data is being organized about what you're doing. That is, thinking ahead of time about how important different types of files are and the steps you are willing to take to insure the safety of the most important files.
One specific thing I suggest copying from Leo, is the use of TrueCrypt. Like him, I too use it for encrypting data at rest. I also use it to encrypt the portable applications that I have come to depend on every day such as Firefox, Thunderbird and an FTP client.
There is a portable version of TrueCrypt that, after years of use, I can attest has no downside at all. I can't even recall if I've ever "installed" TrueCrypt on any computer where I've used it.
TrueCrypt also works fine when running as a Windows limited/restricted user. In Windows 7, the operating system prompts for an administrator password. In Windows XP, it's a bit more manual, you have to right click on the EXE and opt to run it as an adminstrator user.
One Laptop, Two Copies of Data
Finally, let me suggest an approach for multiple copies of data even when you only have a laptop at your disposal - an internal memory card. If your laptop has a memory card slot, it's a great place to backup hard drive resident files.
You can, of coures, do the same thing with a USB flash drive, but having the backup media fully inside the laptop makes a huge difference, at least to me.
The only downside to this are some netbooks where the memory card sticks out a bit even when fully inserted. Samsung, I'm talking to you.