I don't stock many parts that might involve what I would consider a major repair. Mainly just routine service items. Like several here, I try to keep piece of mind by maintaining my bike and carrying things that might come in handy on the road.
Both relay types, fuses, ignition bypass kit, extra throttle grip, tire repair kit and CO2 cartridges, tire gauge, volt ohm meter, electrical tape, flashlight, spare EB relay, scotch lock wire splices and small piece of electrical wire that could be used to bypass a clutch or side stand switch, a compact condensed set of tools and hex wrenches, a pdf of the service manual on my phone and electrical circuit diagram.
It sounds like a lot but I have it all neatly confined to 2 or 3 plastic containers in the bottom of my panniers. I'm still considering an extra pull throttle cable and clutch cable. Anything major, I rely on my road service policy from Good Sam's
I may be a little over the top, but it's not like you can find a Triumph dealer on every corner and the ones you do find don't carry much for parts. I would hate to be stuck along side of the road for want of a few simple parts I can easily carry.
There isn't much I can't handle on the road with this little set of tools.