Bike (fit is very important; disc brakes required)
Pedals, Flat or Clipless
Floor Pump for the home
Hand Pump for the trail
A few Tubes
Patch Kit
Lubricant for chain and pivots
Multitool -- small with allen wrenches (hex keys) and screwdrivers
Camelbak or similar hydration system (smaller packs are great for racing) or Water Bottles