Before you go mountain biking, be sure to bring along some standard items each time to avoid problems. It is essential that you have tools, supplies, food and water. Since you won't want to carry any extra weight, only take what you need. With careful planning you can be prepared with a minimum of items.
Most important is to have a spare bike tube along with the tools required to change it. There is nothing worse than a flat tire, especially if you are well into your trail ride as it can make for a extended walk back. You could run out of daylight if your flat occurs in the late afternoon. Nobody likes getting stuck in the dark, especially when a bit of prevention and planning can avoid this. Bring along a spare inner tube with the proper valve type, either the schraeder or the presta. Make sure you also have 3 tire levers to remove the tire and a bike pump. To really be on the safe side you could also carry a tire patch kit in the event of a second flat tire. Change a tire at home so you don't have to figure it out while you're out on the trail.
Bikes are put together with allen bolts, so a set of allen keys is a good idea. Riding rough trails over long distances can sometimes cause bolts to loosen. You may also want to make an adjustment (brake lever positioning, for example). Allen keys are inexpensive and don't take much room at all. More mechanically inclined types may want to take along a chain tool as well, in case your chain breaks or an adjustment is needed.
Make sure you bring enough food and water for your mountain bike ride. A great compact snack to bring along are powerbars, as they prevent you from running out of steam. If you ride when you are tired your risk of becoming injured is greater due to lack of attention. A good supply of water is critical to keep yourself properly hydrated. You can carry frame mount water bottles or use a bladder setup like a Camelbak. In addition to carrying your water, a Camelbak has storage space for tools and spare tubes.
Always make sure you are dressed appropriately for your mountain bike ride. Keep in mind you will warm up quickly after starting your ride, so don't wear a heavy jacket that you'll end up removing it after 15 minutes. It's best to dress in a series of light layers. Keep in mind that if it's wet or cold, your feet and hands will feel the cold the most. Wear riding gloves and socks suited to cycling. Your local bike store can assist you in selecting the correct gear for the kind of riding you will be doing so try and establish a good relationship with them.