Note: this article is a work-in-progress so at the moment is not an exhaustive list.

These are the minimum things I take for lightweight offroad cycle touring without resupply (eg. going bush nowhere near towns).

Tools

pump - I take a (109g);
chain breaker;
T25 torx wrench (brake rotor bolts);
allen keys in 2.5mm, 4mm, 5mm and 6mm;
spoke wrench (make sure you take the right size for the nipples your wheels use);
leatherman kick which provides pliers, side cutters, knife, phillips and flat blade screwdrivers, bottle and can opener;

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Spares

tubes (x2) - even if running tubless - a sidewall tear without a spare tube could be a disaster;
drop-out/derailleur hanger;
SRAM or KMC joiner link;
gear shift cable (long length so can be used for front or rear);
a few strong zip ties;
small roll of gaffer tape - invaluable - can be used to repair many things including tyre sidewall cuts, holes in shelter (fly, text, bivvy bag), disintegrating shoe soles!
5m of 2mm dyneema cord - this stuff weighs almost nothing but is amazingly strong. Good to use for rigging an emergency shelter or wrapping around things to hold them together.
spare spokes and nipples - my wheelset has three different lengths so I take one of each length.
gaffa tape - don't take a whole roll. Just wrap some around your seattube, stem or a tube on your frame. Many uses - repairing a torn tyre sidewall, rip in tent or clothing etc.;

cigarette lighter - the ability to get a fire going can be critical if you're stuck out overnight;
fire lighters - a couple of fire lighters can make all the difference in getting a fire going and they weigh next to nothing. Keep them separate from your other stuff in a sealed zip lock bag. The chemicals are nasty.
space blanket - overnight shelter or to keep warm and dry while waiting or repairing you're bike on the trail;

suture strips - highly adhesive strips that can be used to hold cuts together;
assorted band-aids;
alcohol wipes - good for cleaning out cuts and abrasions. Best ones to get have iodine as well;
compression bandage - really useful when its snake season;

Here is a list of things that you may take but that you can get away with not taking:

tyre levers - I leave these at home because the tyres I use (Conti and ) can be taken on and off by hand;
shock pump - air suspension is pretty reliable nowadays so I don't normally take a shock pump, although before big trips I may bring forward a just to be sure - note: service your suspension at least a week before the big trip to make sure everything's working properly before you go;