I haven't dabbled into the world of cloud storage for backups yet. The only one I really use is Google Drive as it's handy for quickly transferring files from my Android devices to PC's...
You point out a common fallacy about data in the cloud. Cloud storage and cloud backup services are completely different beasts. Cloud storage is just that—storage only—and is not suitable for backups. While there is some cloud storage that is reasonably secure, you will have to shell out some shekels for them. The free ones are rarely secure and are subject to disappearing with inadequate to no notice at all. Google is notorious for discontinuing free services with inadequate notice if it feels it could make money off them if they weren't free (or they feel they are losing too much money on them). Google is also infamous for snooping. I would be very surprised if Google wasn't marketing personal data it snoops from Google Drive (do you really think it is "free"?).
Also, unless you encrypt data yourself before uploading it to a free cloud storage site, it is not very secure.
Reputable paid cloud backup services, on the other hand, are reliable and secure. The companies running these sites know that their bread and butter (the fees their users pay) would go south if they were lose their customers' data or if it were to be hacked. While cloud backup site store data, the data stored is essentially a mirror of data that is kept on your computer instead of being a sole repository of that data. Data on your computer is encrypted before it ever leaves your computer and you hold the key (generally, a password) so the even backup site cannot access your data. In addition, the cloud backup site adds additional encryption to their servers for an additional lqayer of protection.
Basic plans will use only one server to store your backup. The more expensive plans will store your data in multiple servers physically located hundreds of miles, something called georedundancy. If one server gets knocked out be a disaster (one heck of a disaster since they have backup power and A/C systems at each server), your data will still be safe on one or more other servers.
Cloud backup services I recommend include Carbonite.com (my personal choice though they all have their own advantages), CrashPlan, and Backblaze.
...It's something I might consider in future, but with the amount of data breaches happening these days, it puts me off a little...
I don't blame you for being cautious (heck, caution is usually a good thing) but reputable cloud backup services are as secure as anything you are likely have in place yourself. They are no more likely, probably even less likely, to get hacked than you are.
...I keep two offline encrypted backups at home and have a backup stored in another safe location.
That alone is an excellent backup scheme, securitywise, probably better than mine since my local and offsite backups aren't encrypted. It's similar to mine, which is a set of four backup drives for every data drive in my computer: two drives of each set kept in a drawer in my bedroom away from the computer and the other two drives kept in my safe deposit box in the vault at my credit union several miles away (that vault is reinforced concrete built on solid granite bedrock; I saw it being built). I swap out the onsite and offsite drives no less than once a month.
Since any data I change or add after I put the offsite drives in the vault will also be lost if I lose both my computer and the onsite drives, I also have a basic Carbonite account that automatically uploads new and changed data on the computer shortly after it is created or changed (I can also 'tell" Carbonite to immediately upload data if it is critical and not otherwise recoverable). I could recover all my data from Carbonite but it would take forever to download whereas I can more quickly recover most of my data from my offsite drives, then recover the more recent when from Carbonite in much less time that downloading all of it.
The basic plan of Carbonite will not automatically upload large files, although they can be manually uploaded, but the only files I have that large are video files from recorded TV shows and I'm not worried about losing them (pus my ISP would have a cow over the high amount of upload traffic that uploading all them would cause). Also, certain file types, such as .exe and .ddl, not only have to be manually uploaded, they will have the file type changed. the only files like that I want to backup are program installation files (which I save on my computer). I get around that restriction by either adding .disable to single file installation files or by zipping program installation files that use multiple files. Those will automatically upload and are more easily retrieved.
Another advantage to my Carbonite account is I can retrieve my data from anywhere I have a secure internet connection. This is handy when I'm on the road since my little notebooks have only 500GB of capacity so I can't carry all my data with me (nor would I want to).