Flat-Resistant Bike Tires
There is a lot to be said about this subject (read more). The short story is this: Get yourself some Continental Gatorskins and spend your time riding, not changing flat tires. Update - 1 year on the Gatorskins and not a single flat yet on Seattle streets, through lots of broken glass, thorns, etc.
Gloves keep your hands warm on the cold days, clean and comfortable every day. If you stop to tinker with your chain or change a tire, let the gloves get dirty, not your fingers. Plus most bike gloves have padded palms for vibration absorpion and they are great for wiping your chin after a sloppy SNOT ROCKET.
If you're riding in the dark or rain, you need lights. 60% of adult bicyclist accidents come from riding in the dark without lights [citation]. A red blinker on the back and a white LED headlight on the front are plenty. More about safety on the Safety Page and more about lights on the Lights Page.
Commuter Rain Gear
There is a whole page of information about riding in the rain, what gear to get and why it is not half as bad as it sounds. See the Rain Page.
If you get a flat tire, you'll need to be able to change it. Good news, it's much easier than on a car. These are the essentials: Tire levers, pump, spare innertube. I also carry a multi-tool which includes varying sizes of hex wrenches and sometimes a screwdriver too. You never know when you'll want to tweak a rattling fender or tighten a loose seat post.
Don't trouble yourself with a rain cover, they leak, fly away and are otherwise annoying. Get a waterproof bag and be done with it. Nothing like nice dry clothes when you get to work. More info on the Rain Page and the Bags Page.
Get a big bag of 'em! Throw a fresh one in your pack every day, and freshen up when you get to work. No shower required. You will feel fresh and clean all day, I promise.
velcro ankle straps
Keep a couple of these in your pack, even if you intend to ride in shorts. You never know when you'll need to take a quick spin in your good pants. They can be a life saver, at least a pants-saver.
I carry a bundle of large zip ties (wire ties) with me on every ride, and I have made many repairs on the road for myself and for my friends. They are the cyclists duct tape. Don't leave home without 'em!