I use
Carbonite. Basic plans start at $59/year. For that, you get unlimited automatic backups that work in the background so your computer won't be slowed down while using it. The data is encrypted before it leaves the computer (even Carbonite personnel can't access it) and is transmitted to and from your computer via a secure (https) connection. You can access your data from any computer at any time. It also has thirty day versioning (it keeps any deleted or changed files for thirty days before deleting them). More expensive plans have more features.
The downsides are data transfer is slow so a 24/7 broadband connection is recommended and it cannot be used to store data that isn't on your computer. The slow data transfer rate is only a problem for the initial upload but, once that is finished (it can days or even weeks for the initial upload), it really isn't a problem.
A word on archival. It is a very bad idea to store data in only one place, be it on a HDD in your computer or in cloud storage. At the very, very least, each piece of data should be duplicated in at least one other place different from the original with at least one copy stored locally and one offsite. I always recommend storing one backup copy off the computer but still easily accessed, such as in a different place at home where the computer is, and one copy offsite, such as in a desk at work, at a neighbor's home, in a bank safety deposit box, or in a paid online backup service. The reason I specified a
paid online backup service is free web storage sites are notorious for disappearing with little or no warning, taking your data to computer never, never land to be seen never more.
Carbonite can be used for your offsite backup as long as the data also remains on your computer but you should also have a local backup as well. If you feel that would be too expensive, consider how much it would cost to recover your data if it should get lost. Data recovery from a failed HDD is iffy at best and can cost as much as several thousand dollars. Some things, such as photos and many documents, can't be replaced if the data can't be recovered from a failed HDD. Believe me, keeping multiple backups is much less expensive.