Dropbox is the first name that comes to mind. However, you must not rely solely on a cloud solution. The best thing to do is get an external hard drive and store your backup on that drive. Then store that drive somewhere off site such as in your office at work, in a detached garage, at the home of a family member. You can encrypt the data if you're concerned about leaving the hard drive unattended or with someone how may try to look at the images/data.
The problem with cloud solutions like Dropbox and Google Drive is that it takes a huge amount of time to upload and download data. If you have many terabytes of data, you will likely receive an overage fee from your ISP. Contact your ISP to find out about your upload/download limits before you get charged any fees.
The other problem with cloud solutions is what happens if the company suddenly, and without warning, goes out of business. Your images are lost. Usually when this happens (e.g. Google Plus) you get a warning well in advance, but things don't always work this way. So you really need to have multiple types of backups. Have a backup on the cloud like Dropbox or Google Drive, and have an external drive stored off site. This would be the best solution utilizing best IT practices.