The vision of http://sandstorm.io ties well into this strategy (not affiliated, I just like the idea).
Hopefully, your data should not be throwaway. The common architecture is to have an application server inside container that connects to database or other persistent storage running outside containers.
At that point you can argue there is no point in using a container, but your statement is false.
If you can't guarantee that, you are going into the world of NFS (which databases do not like much) or iSCSI, or, if you have distributed storage, into the world of glusterfs, ceph or something similar.
It's much simpler to just set up a database server (or cluster) and live with that.