Without knowing how long or where your commute is, it's pretty hard to say what is "essential" other than the bike, and some way to carry stuff.

Beyond that, we need more info. But, in general:

1) A helmet, if you are a helmet believer.
2) A lock - otherwise your bike is gone and everything else is irrelevant.
3) Lights - if you ride in urban areas, a front and rear blinky, to be seen day and night. If you are absolutely sure you'll never ride at night (as in, you'll take a taxi or bus home), or you ride in very well-lit areas, that would suffice. If you are riding at night and there is not enough light to see by, you need a good "to-see" headlight also. The Planet Bike Blaze is a good bare-minimum light, and the sky's the limit from there.
4) Tools and such - again, if you are riding in an area with public transit or taxi service available as a fall-back, I'd go very light on this stuff. The mini tool is always useful, and I'd buy really good flat-proof tires instead of hauling a pump and spare tube with me every day. However, if your commute is 20 hilly miles out in the country, you'll want fast tires, and ability to get yourself home no matter what happens.
5) Fenders - If you are in Phoenix, fenders are less important than if you are in Seattle. Also, you may decide you don't want to commute in the rain, and employ alternate transportation those days.
6) Stuff hauling - you might want to try the basic messenger bag or backpack for a while, and then see how you might want to change your hauling strategy, if at all, once you have a better idea of your needs.