If I'm out of town I carry pretty much extra everything, but if it's local I quit doing it because in all my time playing local I've had exactly two breakdowns and both times I've been lucky enough to still be ready on time. I've been fortunate enough to have never had my vehicle pillaged but I know enough other folks who have that it's a real possibility so I quit loading my ride down with duplicate stuff when I'm close to home. IME, it's mostly amps that lay down at the wrong time, so I tend to carry two heads most anywhere, but they will both be in separate 2U cases, or these days a small waterproof box.
Speaking strictly to basses, most of what I'm using today are parts basses I've assembled myself so I know they are sound, that the solder joints are good, etc. In short, I'm confident they will hold up under normal wear and tear. I also keep a close eye on my bass when it's out in the wild, and always pick a spot where no one has to get too close to get on or off the stage. The only time I go anywhere without a stand is my brother's place. He's got a couple of those multi stands that knock down to suitcase size and there's usually an open spot, otherwise it is strictly on me to have a stand, and use it. But yea, after never needing one I just quit carrying a backup bass locally.
I know that every day I don't have a breakdown only puts me one day closer to that event, but the same is true for a vehicle break-in so I rolls the dice and takes my chances local then run the risk out of town.