I think it's important to have a rear rack with a trunk bag to carry your wallet, keys (it's uncomfortable riding with these things in your pocket), cell phone, any cable lock you might have, spare tire, mini pump, patch kit, multi-tool... okay, so I don't like to leave the house unprepared
You will need other things if you are planning to go above and beyond normal riding. If you are planning on riding great distances, do yourself a favor and get bar ends. Also, a bike computer is a fairly cheap toy that can make riding more fun.