Yes you can but if you have a lot of files, a flash drive won't back it all up. If you only need to back up 32GB-64GB for example, you could back it up on the flash drive. However, anything bigger isn't sensible for flash drives; you're better off getting an external hard drive. Also, it's not a long-term storage option––it can corrupt easily or be lost.
Many types of USB drive, sometimes referred to as a thumb drive, also have handy features like a key chain ring or a small LED flashlight. Some can even transmit your data wirelessly for the ultimate in digital convenience. And as with any fun accessory, there are plenty of novelty versions of flash drives designed to show your personality, display your sense of humor, or broadcast your team loyalty.