Uploading your whole hard drive online will require considerable storage capacity. There are several online services available, such as Jungle Disk, CrashPlan, Carbonite. These charge monthly and yearly fees and provide different storage packages. Unlimited storage usually costs around $5 per month or $50 a year. Take your time and go through the packages offered and choose one suited to your needs.
If you are looking to back up digital media, you will need more storage and the unlimited storage option would serve you well. You can sign up with any of the online data backup services (some also offer trial periods) and download their clients. These software clients manage data exchange from your computer to the online server.
However, if you are simply looking back up your important documents, you may want to go with a cheaper (or free alternative). Microsoft’s SkyDrive offers up to 25 GBs of storage capacity which you can use to store your documents and files online.
Google Drive is also an excellent option to backup important documents. These can also be accessed, edited and shared directly online. Protection of your documents in the free services mentioned above depends on your account security (Microsoft Live or Gmail) since these are linked to your accounts.
Most ISP services also provide online storage for hosting your files. If you have access to FTP storage space you can create a new network place and copy your documents to the online storage. This however is not so secure a method and usually storage space is limited.