A lot of good points on here. I personally did not want to add any large storage containers unless necessary. I have a Polaris Sportsman 850 with the Factory front storage box and small rear glove box and it is more than sufficient. I've also never really needed much after thousands of miles. I've actually needed it more for other people who were not prepared with anything!
That being said, a winch on the machine is cheap insurance, so is an extra at least 50 ft of line to get you further one way or another has helped me. It's amazing how 50 ft on the winch isn't very much when you're in a mud hole somewhere. I also switched everything out for synthetic rope. Also have a tree strap and snatch block, with a couple shackles. Sometimes I will bring a gallon of extra gas if we are going on a long trip and unsure of availability to refill.
Basic tools for stuff that is actually on the machine helps. I don't go overboard as there's not really much you can do on the side of the trail. I have four cheap ratchet straps, extra face mask for really dusty conditions, bug spray and suntan lotion, plug repair kit with about 10 little CO2 canisters. It took me three to fill a flat one day for another guy. About 20 foot long zip ties. First aid kit, 10 ft of quarter inch line for siphon hose, small roll of duct tape. I like to be prepared, but not overboard. Be honest with yourself, your abilities, and where you are going and what you are doing. Like others have said, good tires are a must. Go 8-ply.