This is possible only for certain stereo tracks. When the vocals are exactly the same on both stereo channels, you can remove them by “subtracting” one channel from the other. This works for many studio recordings, where the vocal track is mixed exactly in the center.

To do this in Audacity:

Import your stereo file into Audacity.
Open the track menu (click the arrow next to the track title), and choose “Split Stereo Track.”
Select the lower track (the right channel) by clicking it in the area around the mute/solo buttons.
Choose “Invert” from the Effects menu.
Using the track menus, change each track to “Mono.”
Press the Play button to hear the results. If you are lucky, the voice will be gone but most of the other instruments will be unaffected, just like a karaoke track. You can use the Export commands in the File menu to save the results.