Listed in order of importance!

Helmet
Eyewear
Lock
Water Bottle & Cage
Slime
Pump
Spare Tube
Tire Levers
Patch Kit
Multi-Tool
Seat Bag
Lights
Reflector Set
Fenders
Kickstand
Floor Pump

Additonal Items to improve comfort and enjoyment :

Gloves
Cycling Shorts
Handlebar Ends (for bikes with straight bars)
Aero Bars (for road bikes)
Bike Computer (odometer, clock, speed, etc)
Rear Rack
Saddle Bags (Panniers)
Cycling Shoes
Clipless Pedals