Both Google (GMail) and Microsoft (live.com) mail services offer storage for free, for 5, 10, 15 GB - sorry, I forget how much they give, and the amounts are likely to increase every 6 months from now on...
If you get a subscription to Office 365, then Microsoft were offering 1 TB (1000 GB) 'free' storage but it may go to "unlimited" storage next year.
Google provides a download so you can have copies of everything on your home system (Windows or Mac) duplicated on the 'Google Drive' space, ie kept in sync. I have not yet investigated the Microsoft offering (if any) for my {elderly} iMac. On Linux, I can open a bookmark on a remote server and just drag and drop files either way. I have my external drive plugged into my linux notebook {it has only 4 GB of free space, the external drive is 500 GB} and backup some of my files with that. The Asus EEE is only using about 35-45W so can be left to copy files for days at a time with limited electricity cost.
Add a third "in the cloud" backup service like Amazon Glacier and you have a belt and braces solution "in the cloud" at very low cost.
Glacier has fees, but on the basis of slow transfers - hence 'glacier' name - they will store tens of GB of data for a few dollars a year - I think my estimate for 100GB were about $12 a year. It's designed as a long-term 'retrieve if your home/ firm had a fire' situation ie not expecting daily downloading, but accepting archiving of quantities off your system, whether that be small (daily updates), medium (weekly) or larger (initial copy of all your data).
Amazon don't supply a backup utility but the small investment and your own choice means you could go for one which encrypts everything (so even if someone hacked the Amazon storage, your nude photos from that wild swappers party won't be visible!)
Only kidding about the party photos, but it does mean private documents can be kept securely as they would not be easily readable. I won't say encrypted files are impossible to decode, but the effort is unlikely to be made unless the authorities believe you have really important info, not a few {thousand} holiday and family snaps.
For many people with limited storage needs an external drive is overkill, because these days they store 1000 GB and up (2000 and 3000 GB going under the 100 pound mark). A ten quid USB stick with 16 or 32 GB would hold most photo collections, I'd have thought, but if you want to store copies of music and video (from CDs and DVDs), then you may want lots more, to cope with the quantity of data, and online services would be poor value and slow {costly because of storage demand, slow because of upload speeds on most any internet connection being limited to 20 Mbps at present}.