I have yet to break a string live or from regular playing, but I have had basses and amps stop working at shows. You should ALWAYS have one extra bass on stage with you incase one of them just stops working. I also have a backup amp head with me at every show I do. Whatever amp I like, I make sure to get another one - expensive, yeah, but so worth it. Especially when one of them overheats, something stops working, you need to be able to keep going at the show.
I have extra basses, cables, amps, a box full of tools to fix the basses if there is a problem and I also have two 410 bass cabs with me at every show. Sometimes the extra cab is used by my guitarist because his combo stops working.
Honestly though, all of my backups have come in handy. You can't trust gear to be 100% every night no matter what.