I've only had one chain snap on me in maybe 50,000 miles and that was because I'd attempted to re-join a chain using the original link pin - silly me.
I know carry a chain spliter tool and something like the KMC Missing Link in 8s, 9s and 10s (in with the puncture repair kit.
NB - some say the KMC link should only be used on KMC chains but I've used them on Shimano and SRAM chains with no issues.