With the Internet, you can not only access a USB storage device but the whole remote computer. There are many ways to access the USB drive through computer network. In Windows PC you can share the drive and enable Remote Desktop connection. There are also many software available for that, including TeamViewer and USB Redirector.
USB Redirector application allows users to access any USB device on a network. Two versions are available: USB Redirector Lite Client (freeware) for client computer and USB Redirector (shareware) for server computer.
You need to install this tool on both the computers (server and client) and connect to the Internet. Then connect the USB drive to your PC on the server side, run USB Redirector and then share the USB drive as shown in figure. Run USB Redirector Lite Client to connect the server side. Provide the server IP address and host name in the client computer.
If connection is successful, you will see the list of shared USB devices. Select the USB device you need to connect to and then press Connect USB Device to access the files.
Another method to access USB storage files is a router with USB port. Connect the USB flash drive to your home router. Some routers come with a USB port where you can plug in a USB device and then access its data. To get this setup working, you need to enable remote sharing or setup dynamics DNS (domain name system) on your router.