Updated. Doug made a great point about pumps in the comments. (In fact, I have a CO2 pump, myself.)
To commute by bike, you need a bike. What else?
Bike — More on choosing a bike later
Tail light — Required by law when riding after dusk
Commuter head light — Required by law when riding after dusk. Important even if you don't need the roadway illuminated. A (relatively) cheap commuter head light will let people ahead of you know you're coming.
Lock — See tip of the day, below.
Rack and pannier — You're going to carry stuff. Do your back a favor and carry it on the bike. (A pannier is a special bag that attaches to your rack.)
Fenders — Even if you plan to ride on nice days only, you're going to get stuck in the rain. A front fender keeps your shoes dry. A rear fender prevents you from getting a stripe of road grime up your back. And, a rear fender keeps your pannier dry.
Tire kit, spare tube, and small pump — You're going to get a flat. As Doug says in the comments, get a small C02 pump. Quick and easy way to inflate your tire and worth the extra money. Not necessary if you don't know how to change a flat tire.
Bike computer — It makes riding a lot more fun when you know how far and how fast you've gone.
Powerful head light — Useful if you're planning to ride much after dark on roads that are not illuminated. They can be expensive, but they're worth it if you need it (say when you have to ride across Weston on Route 30).
Buy a good solid lock and leave it on or near the rack where you'll leave the bike at work. Odds are you won't stop between home and work and work and home, so why lug a heavy lock back and forth. If you do plan to stop, carry a lightweight nuisance lock for those times when you have to grab groceries.