Sometimes I carry one, sometimes I don't. I've never had a chain break on the roadie or the MTBs during a ride. When I carry the chain breaker it's because it comes attached to the multi-tool and I want to carry hex wrenches. I have had the need to use a hex wrench many times.
For those who are interested, I use a Topeak Hexus II. I use it when I work on bikes and have broken many chains with it of all speeds, 7, 8, 9 and 10, Shimano, SRAM, Campy and KMC. I don't know what problem the previous poster had with a ten speed chain, but I used the Topeak many times to break a ten speed Shimano chain and reassemble it. The first Topeak I bought I wore out the chain breaker (flattend the tip). I now have a second, newer Hexus II. If anyone is looking for recommendation, which unit to buy, I would rate the Topeak Hexus II as a unit you should consider as it's performed very well for me.