Water bottle cage(s) and water bottles - always take at least one bottle of water with you
Helmet
Floor Pump
Under Saddle bag with spare tube, mini pump and/or CO2 cartridges
Knowledge to use above spare tube and pump/CO2 to change tire
Blinky light for back of bike, to be used during day rides on roads
Bike computer (optional) to track mph and miles ridden
Lock (optional) if you plan on leaving your bike outside

Happy trails and enjoy your new bike!