Only if you have a NAS, but they are usually not cheap and don't support writing to NTFS file systems - only ext3 and FAT32. Otherwise it needs to be mounted on a computer with an SMB server (Windows, OS X, and Linux/BSD all have SMB servers).
But just leave the computer it is plugged into power on all the time and network share the drive.
In windows
Open My computer, right click the drive and click properties
Then click Sharing/Security,
Share the drive and give it a name like 'hdd'
Allow file sharing on your software firewalls and determine the LAN IP address of the computer (or use computer name)
Hold winodws key + r
cmd
ipconfig /all
Then on another computer open Windows Explorer (not internet explorer)
and in the address bar type
\\{IP address on Computer with Ext HDD)\{shared drive name}
ie.
\\192.168.0.100\hdd
or computer name
\\Server\hdd
You should then see the drive