As a drummer, I brought a load of extra sticks, and that was about it. I think my stick bag may have had an extra clutch and a couple of felts in it.
I never really had any spares to bring; I was always the guy who just owned the one kit I used. I couldn't justify the expense of space to store extra snares, pedals, cymbals, etc, so once I bought something new, the old gear was sold off (unless it was being replaced because my caveman technique had broken it).
I've gotten a bit better though. These days, my main instrument is bass, and I will bring extra cables, a spare set of strings, an extra strap, a fresh 9V battery (active bass ftw), and a DI box in case my pedalboard takes a complete nosedive (so that I can at least send some sort of signal to FoH).
For local gigs where I'm driving myself to the venue, I'll even bring a spare bass just in case (get it, because it's in a case?).