External Hard drive
This is one of the most recommended types on backup. One that I'd recommend to anyone myself.. Having an external hard drive is cheap. $75 for a 250GB USB external drive. You can carry it anywhere and use it with any computer. It can store so much information. Some actually have an automatic backup software that allows you to schedule backup on regular basis ensuring that you are always up to date. The down side to external hard drives is that a lot of people think it's a bit pricey. There are other options though.
USB Flash Drive
Also known as a thumb drive, this small device is a whole lot cheaper and easier to carry around than an external Hard Drive. Many people find it stylish to use it as keychains or pendants. It's even become a necessity for a lot of students because of its portability. The USB flash drive is the best option if your looking for a smaller cheaper storage device. 16GB is the biggest you can get for a device like this. This should be enough for a few pictures and music.
I've been saving my files to CD's and DVD's since the turn of the century and for most people they find it more convenient to save files on a disc. The problem with writing to discs though is that CD's and DVD's are so fragile and have so little space for backup. Burning information also takes a while. A standard CD has a diameter of 120 mm and can hold up to 80 minutes of uncompressed audio (700 MB of data). A DVD-R typically has a storage capacity of 4.71 GB.
I actually wrote about this before. An online data backup like Dell Datasafe is for people who don't want to spend to much and don't want to carry around a bulky hard drive, a tiny Flash Drive, or don't want the clutter of discs. Online backup is perfect for a purely electronic way of backing up data. This is actually the last thing I'd recommend to anyone because you would have no access to your files if you don't have internet connection.
It's a bit advanced, but creating a separate partition in your internal hard drive for backup has been a technique done by my ancestors even before I knew what a computer was. But creating a separate partition is easy once you learn it. This allows you to have a backup inside your own computer. When the time comes that there's a need for a re-format or a Windows Re-installation, all your files will be safe in your other partition.
So the next time you get in front of your computer, ask your self if you already have backup for your files. You never know when you'll need it.