I moved my iTunes library around a bit, so I don't know the canonical path. Just adjust the URLs you see in this answer.
Configure Firefox to handle audio/mpeg using iTunes:

Then, open a URL in Firefox such as (on Mac OS X):
file:///Users/username/Music/iTunes/iTunes%20Music/Artist/Album/Title.mp3
and it will play in iTunes. Since it's already in the library, it's not added again.
Using a browser like Firefox (not IE) has the benefit of being able to browse the file system if you want, and clicking on a file then opens in iTunes.

Similarly, in OS X Terminal, you can use the following:
open -a iTunes file:///Users/username/Music/iTunes/iTunes%20Music/Artist/Album/Title.mp3
It will use iTunes to open the URL, playing the file.
I don't have a Windows system with iTunes, it might work from Explorer if you use iTunes as default application for .mp3 files.
Via here, the following could work:
rundll32.exe url.dll,FileProtocolHandler file://c:/wherever/iTunes/library/is/on/Windows/file.mp3