Use a USB drive. For small amounts of data or data shared between computers a small USB drive can be just the thing. The files can be copied to the drive and kept safe.
Save it online. There are many online file storage services. Dropbox, Box.net and Carbonite to name just a few. Search for online file storage and you will find many to choose from, free and paid. Services like Carbonite offer automatic back-up and can be accessed from anywhere. This is a good feature if you want to back-up your files without worrying about it.
External hard drives. Today's choices for external storage are small portable and relatively inexpensive. They are a great choice for backing up all your data in one place and work well as an archive for photos, files and documents.
Burn it! Another choice is to burn data to a CD or DVD. This is great option for data archiving that is not likely to change or needs to be stored. Photo albums on DVD can also be kept with scrapbooks or other documents.