Seat or handlebar bag, 2 replacement tubes, tire removal irons, pump, a small cut-out section of old tire to use inside the tire in case of a casing rip (I never had to use it!). Small adjustable wrench or 'bike tool combo', allen key tool combo. A few paper towels to wipe grease / oil off your hands. Small first-aid kit.
Because I generally ride in town and on multi-use paths, a good, loud bike bell is an essential piece of safety equipment for me.
I have a rear rack with a bungee net on which I keep my lock/wheel cable and can attach panniers to go shopping, bring my books to class, and so on. This weekend, I'm even planning a light bicycle camping trip with my partner. As a result, racks and panniers are quite vital to me.
Fenders don't keep you dry in the rain, but they do keep you from getting too muddy, and a decent set will keep mud from caking your mechanicals, so they're a must if you ride in all kinds of weather.
Last but not least, a good pair of lights. After years of attempting to make do with $20 lights, I eventually gave up and purchased a Cygolite Metro 400 and bike air filter here. I quickly switched to a Light and Motion Urban 800 after that. Another crucial piece of safety and utility equipment is a lamp with at least 300 lumens.