If your router accommodates a USB drive (memory stick, or external HD), then you usually can ftp to it.
For example, I use a NetGear WNDR3700 router, and attached a 4 GB memory stick to store ftp'd camera images while testing the cameras.
Also, you may then be able to set up for access from outside the network. However, this does NOT form a server per se, but only a data repository. A real server allows, for example, running php scripts to select and display images.
I've tried a (now old) Maxtor Shared Storage device with mixed luck.
If you don't mind having a computer running 24/7, you can configure a server in your computer - Macs do so very readily.