On an ILS approach, if the GS fails, you must execute the missed approach.
Why?
Think back to your approach clearance..."Cleared ILS Rwy 17". You weren't cleared for the LOC.
I don't know the contingencies available to ATC. If you report the failure, can they immediately clear you to continue via the "ILS Rwy 17 LOC only"? Or are they required to have you execute the missed? This I don't know. I tend to think that they will send you around if you're IMC.
In the case of an inoperative GS before you commence the approach - I have been cleared for an "ILS Rwy 17 LOC only" approach before, Part 121.
EDIT: Oh yeah, since this is in the pre-interview forum, I just thought I ought to mention that if you are in a sim ride at an airline interview, and this happens, and you continue using the LOC only, don't plan on working there.