I don't carry all of this stuff on the actual machine, but have it back at camp during an out of state trip. This at least gives me the chance to fix the machine before the next day.
Axles - The fronts are different left to right, but the rears are the same, so I have a total of 3 axles back at camp. Breaking an axle normally doesn't disable the vehicle and you can continue to ride, or at least get back to camp, without a ton of issues. Most of the time you don't even have to do anything with the axle but sometimes it will break to the point you have to remove the pieces.
Obviously if you are in the middle of a really tough trail it can make it more of a pain. Breaking a rear axle is a little more of an issue than the front because you get some weird handling issues...if I was real concerned I would carry one rear axle on the machine.
Belt - Keep one at camp but don't carry it with me on the trail. Not much of an issue on these machines, especially if you replace them at home on a regular basis.
Tie-rod - I do carry a complete tie-rod assembly with me. Pretty small and one of those things that will disable the machine on the trail if you break one....or at least makes it a huge PITA to get out of the woods.
Fuel filter - these are tiny so I keep one on the machine....again, go ahead and change it on a regular basis in the garage.
Spark plugs - never carried any of these before but will from now on. Recently had an issue where a plug went bad out of nowhere and the machine barely had enough power to load on the trailer. Fortunately I was still in the parking lot when it happened but if it happened out in the middle of Windrock or Brimstone it would have been a pain to get back.
Air filter - never carried an air filter...guess I've never seen a machine become disabled because of one. I guess if you do a lot of deep water and mud it might not be a bad idea to carry a spare.
Tire repair - don't carry a spare, but a lot of plugs, a couple valve stems, and a small compressor. A small bottle of tire sealant isn't a bad idea either. I've plugged some nasty sidewall gashes with 10-11 plugs and we got the machine back to camp.
Biggest thing is to make sure you have all of the right tools to do the job. No reason to carry a belt on the trail if you don't have the right size sockets to pull it apart! Same thing with the axles and everything else. I would seriously suggest tearing into all of those parts to practice and make sure you have the right tools.