Depending on the type of off-road, weather condition and the distant travelled, I usually carry 2 to 3 litres of non-gasy energy drink in my hydration bag. It is absolutely important to carry more water than needed, as the excess may save life if you lost your way in the forest or helping someone in trouble.
2. Energy bar
I usually carry two high fibre energy bars, which can last me for a day ride.
3. First Aid Kit
This is something I don't wish to use it, but highly essential item. Besides using it for myself, I have helped a handful of riders during the past one year of off-road riding. Some essential first aid items that must be included are iodine and alcohol, which help to kill bacteria on the wound.
4. Inner Tubes
Well, the last thing you want is to push your bike all the way out of the forest. Keep an extra tube in your hydration bag, it will come in handy. For the past one month of riding, I have seen 4 cases of punctured tires, of which one rider did not carry extra tube. Although I ride tubeless tires that suppose to be punctured proof, you never no if one major impact on sharp rock would tear a big hole on it.
5. Tire levels
Some people may be able to use their hands without the levers, but why waste your energy when you can use a simple tool to do it?
6. Hand Pump
Buy a good one, which has the option of Presta and Schrader valves. You never know what valve is needed, especially the tube belongs to someone.
7. Multi-Purpose Tools
Do I need to say more? Chose those that has all the standard size tools for your bicycle components, especially for the seatpost and brakes. You can get it from any good bike shop.
8. Cable Ties
It will come in handy, for any possible situation you can think of.
You may need it in situation when your derailuer failed to work reliably after a rough ride.
For emergency call, or for the rescuer to track you. Keep it in a water proof zip bag. I prefer iPhone as it comes with digital compass and google map that may help you to get out of the forest.
Other not so essential items that you may want to carry along are a piece of cloth for cleaning purpose, and a duct tape for quick repair.