Lots of copies keeps stuff safe!
Follow the Rule of 3 for your research data: have 2 onsite copies and 1 offsite copy. This makes your data safer in the event of natural disaster, theft, device failure, etc.
You have lots of hardware options for storing your data. The best are:
Choose whatever is easily available to you to get to the 3 copies of your data.
Other options for storage such as CDs/DVDs, cloud storage (see box below), and USB flash drive (use only for data transfer) are not ideal for dedicated data storage.
Principles of backups:
Always test your backups to be sure that they work and you know how to retrieve data. You don't want to be learning to retrieve data when you are stressed about losing the main copy of your files.
Don't forget to test your backups, as this story illustrates!
Your data are dependant on a company's business model so read the Terms of Service! Here is an example of Google Drive's Terms of Service:
“When you upload or otherwise submit content to our Services, you give Google (and those we work with) a worldwide license to use, host, store, reproduce, modify, create derivative works (such as those resulting from translations, adaptations or other changes we make so that your content works better with our Services), communicate, publish, publicly perform, publicly display and distribute such content. The rights you grant in this license are for the limited purpose of operating, promoting, and improving our Services, and to develop new ones” (source)
This should worry you. There are good cloud storage providers out there, but you need to read the Terms of Service to know the difference.
Finally, do not store sensitive data in the cloud.