Helmet: This is definitely a must. But these days, you can get cool looking lids inspired by the skateboarding community
Everything-proof jacket: A key element in all seasons. Even on summer nights you'll need something to keep you warm and dry on your way home from the bar
Blinky lights: Red in back, white in front. You're safer if you can see and be seen. Plus, it's the law
Fender: Essential for keeping your ass dry
Rack: Helpful for transporting groceries, pets and other oddly-shaped objects
Sunglasses: Good for keeping bugs and wind out of your peepers. And for looking good/unidentifiable
Beard: It'll keep you warm in the colder months (women should wear scarves or neck gaiters - they're less itchy)
Weather-resistant backpack: Good for storing and transporting all of your bike commuter odds and ends - extra layer, bike lock, change of shoes, thermos of warm drink, laptop, six-pack, etc.
Gloves: If your hands are warm, the rest of you will be warm.
Alterations to your pants cuff: Whether you roll 'em up or incorporate the high-vis reflective strap, you need to keep those cuffs clear of that chainring
Tools to change a flat: You should know how to do this. And you should carry the tools in a seatbag or in your backpack. A frame pump makes this job easier
Bike lock: No, this isn't New York or Philly, but you at least need a minimalist-style lock to keep your ride safe from filthy bike thieves