If you are looking at a single media which you can use for 10-20 years as a backup or storage device, then it will be difficult. All of the current backup solutions require access to a computer and have a shelf life. And a computer generally has a max shelf life of 7-10 years. After 7-10 years getting a new computer which can consume the same media is dicey to say the least.
The best solution is as follows
1) As of today, i.e. 8-Oct-2015, Keep 3 external, non-Flash non-SSD, drives to backup your data. The quantity 3 has been chosen for having redundancy and if one HDD fails then you have the ability to still access your backup.
2) After 3-4 years or when you buy a new computer in the future, look at the most economically backup at that moment of time and move your data to the new backup. This may also entail modifying the file format from one to another. If when you buy a new computer the most economical backup is still a USB HDD then by all means stick to it. But repeat this every 3-7 years when you buy a new computer.
Please note that it is assumed that
the file format that you are using to backup your data will still be around
you will have applications and a matching OS which can run those applications in the future which can consume those file formats.
If you are comfortable with cloud storage then one can use Google Drive and/or Amazon AWS services too. That will also allow you to have data storage if not for 10-20 years then for some years in the future. However if your backup size runs into multiple hundreds of GBs then please factor in the cost of bandwidth and the time taken to upload and download the backup files.
What you are looking for, i.e. 10-20 years of backup, is generally required by libraries or Universities or Government departments. Since these are corporate entities or organizational entities they have agreements in place with various companies to provide them this service. So for example IBM or some other company will have a contract which says, that IBM will backup say 100 GB of data every month for say 7-10 years with certain cost escalation. These companies then maintain the hardware and software so that the data can be accessed. If you are part of a corporate entity or an organizational entity then one can approach these companies. However if one is an individual or a simple retail customer then it is not possible to do so.