Last time I went, I broke two spoke nipples, because I slid down a deep (as in axle-deep) rut where a tree root poked out of the sides. Not a problem, though, I continued on my merry way until I found a bike shop and bought a couple of nipples. I will not carry spokes, though, but I have surmised that a few nipples aren't too heavy to bring the next time around.
As for chain, I haven't bothered carrying anything more than a couple of quicklinks and a few extra inches of chain. Instead I opted for the 11-speed in-hub gear (it runs on oil, btw, not grease), and use a rather strong chain which I can't remember the name of at the moment. All in all, this means less strain on the chain, but I have to say I wonder if a Rohloff 14-speed hub would be stronger or nicer, although I have had no problems with the Shimano.
I use Shimano hydraulic brakes, and they are dead easy to bleed without having to carry anything extra (you can bleed them from the top), and I do carry extra brake pads, as they weigh next to nothing.
My bike is a Bullitt "long john" cargo bike. I find it so much better than most other solutions that I also use it on everyday basis when a motorised vehicle is not needed.
Tyres are Schwalbe Marathon Supremes. On the front is a 1.6"/20", and on the back is a 2.0"/26" (if they made the 20" in 2.0", I would use that on the front = floats better over soft ground).