Major repairs ... hmmmm phone for rescue.
Day to day riding ....
I take the sort of tools I'll need to fix the stuff I've added like DRLs satnav brackets etc
Yes - a tool to remove the front wheel. Probably not in the OE kit because with only a side stand as standard the front wheel is not coming off without heavy duty assistance.
Although I carry a front spindle tool I am sure there is no way of removing the rear wheel with the OE tools unless you are a really and I mean really strong person.
Yes - STOP & GO puncture repair kit with gas cylinders (do not hold in your hand whilst using as I believe they get VERY cold as they discharge. So gloves, a rag or, as I have, a little gun thing that holds the cylinder.
Yes - A 12v pump if you have space ... saw a nice small one in Home Bargains this week.
Yes - screwdrivers, Alan keys and various sizes from a set of spanners that have a 'known use' on the bike ( don't always need a full set)
Yes - Tape, spare fuses, aux supply ( car type cigar lighter) wired or crocodile clipped to battery for Phone and camera charging.
You can't take everything
and sod's law dictates that whatever you don't carry you will one day need
. So I just try to carry the stuff with which I can fix
the sort of things that I'd be mightily embarrassed
about if I had to be rescued while out on a V-Strom ride out.