I'm one of those OCD types who brings backups of everything although it's usually to keep the band going and not really myself. I bring a backup bass head, bass, cords and cables of every type, a mic or two, speaker cable or two, mic stand, been known to throw a guitar combo amp in the car if there's room, and on and on and on.
That's in a situation where it's my/our band and we're trying to make an impression and gear failure has to not happen as there are plenty of other things to worry about. In a hired-gun situation, I will bring a backup amp but leave it in the car, bring in 2 basses and 2 cords.
In the afore mentioned situation, I've used a bass amp as a poweramp for the vocal monitors as well as bailed out countless guitar players, keyboardists by having some little cord that was needed to hook one thing to the other and make things happen or by just having more mics and cords to mic more things and sound better.
I did have to use my backup bass amp one time actually as a bass amp just because I guess I was so focused on covering anything that could go wrong that I covered everybody else but forgot to pack a powercord for my bass amp. My backup (T-MAX) doesn't have one of those power cords that unplugs at both ends like your computer does, the end connected to the amp is hardwired into the amp. So I used that amp because I could plug it in (an important feature in electric amps). No worry's though, it sounds great and still does, was just thumping on it a little bit ago and it will be getting some rigorous use tomorrow night.