A lot of cloud storage providers have a free account with 5-20gb of free storage in order for you to try the service. The aim is to get you to upgrade to one of the paid plans. You can of course register accounts with any number of providers in order to use the freely offered allocation.
There are not usually any tie-ins, such as giving a credit card, so they can be used easily to evaluate the service and to use for back up of relatively small amounts of data. These may provide enough to back up essential documents, emails, or family photos to give peace of mind.
Some of the most popular Cloud Storage providers with free accounts are:
Dropbox
One of the oldest and most popular cloud storage companies. Used extensively by businesses.
Dropbox gives a basic 2GB free, and will increase that with referrals to 16GB.
Google Drive
Powered by Google and comes along with a Google and Gmail account. 15GB of free storage overall.
Google Photos gives unlimited storage for photos of up to 16 megapixels, so is worth checking out if you want to back up family and personal photos.
Amazon Web Services
Amazon offers 5GB of free cloud storage through the AWS account. It does require a credit card to be put on the account, but won't be charged unless the extra services are activated and used.
BT Cloud
This is for BT Broadband customers and offers 5-50GB of storage, or up to 500GB on some accounts. If you are already a BT Broadband subscriber then this is an easy option for some free cloud storage.
Microsoft OneDrive
OneDrive comes with a free Microsoft account and gives 5GB of cloud storage. Students can access 1TB. Another easy option for some free cloud storage.
Box
Similar to Dropbox, Box gives 10 GB storage with a 250 MB file upload limit on the Personal plan.
iCloud
Comes free for most Apple device users, but also available on Windows. 5GB free cloud storage.