I've had two chain breaks, the first when suddenly powering up a short sharp hill... didn't know what had happened initially. Looking behind and seeing this huge trail of chain behind me was quite amusing.
Second time was the very end of last year. Due to the bad weather I'd kept my chain much longer before changing it, assuming that the salt/snow would wreck a new chain. Anyway I was doing a 50 miler on a chain that'd done 4,500 miles (I usually change around 3,500) and had a most exciting moment when a chain part broke, lifted up a piece of chain which then caught on the front chain tube, ripped it off its mountings and into the front gear changer widget. Took me a while to work out what had happened, I thought the chain tube had just disconnected itself on its own. Although the chain didn't completely break so I didn't have the faff of re-threading it through the tubes, when I took it off I noticed cracks in about eight of the links. This encouraged me with the quality of KMC chains - it kept going way after I normally change them, despite several weak spots.