Bicycle messengers have special backpacks, because they have to leave their bikes so frequently. However, most commuters will prefer to avoid backpacks, which tend to make a sweaty mess of your back. Instead, look at the thoughtfully established methods of bicycle touring: using a rack and panniers. Not only do panniers free up your motion, but they put the weight both on the bike and low to the ground, making it far safer and easier to ride and handle the bike.
Our article on panniers will tell you about bike briefcases, bike garment bags, who makes the best stuff in general, and more.
Knobby tires work great on a dirt fire road, but they add terribly to the pedalling you have to do when on pavement. If your commute is mostly on the road, then use smooth road tires, the thinner the better. You will puncture virtually no less rarely than with studded tires.
Also, inflate them to their highest rated pressure to further cut rolling resistance. This will also prevent the most common source of flat tires: pinch flats from under inflation. You'll notice a more jittery ride on rough pavement, especially on a bike with aggressive geometry such as most road bikes, but most riders get used to it quickly to find it no discomfort.
Avoid fat balloon tires unless you only ride on beach sand. I personally have no problem riding on loose gravel or dirt roads and trails on even my ultra-skinny racing tires, and they're tubulars, at that. When I pick up my mountain bike after this kind of experience, "technical" terrains seems trivial. Cyclists who must ride through sand and gravel manage fine with skinny road tires once they learn to handle with them (our article on cornering technique should help). If you ride through rough gravel consistently, look into training tires or other slightly heavier but very robust tires.
Not all fenders are created equal, but any is better than none after a big rainstorm. The main source of muck on a rainy ride is from the road itself, and a good fender can keep your pants from getting spattered with road grime on the way to work, which is certainly worth the cost of a bit of plastic. They're also nice for the guy riding behind you.
Efficient Body Geometry
According to every book I've read on professional bike fit, riders who want to make their ride easier should set their handlebars a couple inches below the seat, with your body leaning forward and so that 45% of your weight rests on the arms. Set your seat to 107% of your inseam measurement.
This will allow you to breathe more deeply, better absorb road shock, improve posture and muscle tone, allow you to use your entire body and all three leg muscle groups (rather than just your quads with the upright posture of many bikes), and improve comfort to boot. A riding position which leans forward about 45 degrees (a flat back is desirable, but not necessary for commuting) will also do wonders for your back by expanding the vertebrae such that the arch disappears, which relaxing tendons otherwise constantly strained by upright walking.
Second, your bike should have dropped handlebars to allow these advantages of proper body geometry. They allow far better muscle teamwork and far better aerodynamics, improve stability and steering, and are far more comfortable. An article on dropped handlebars details the stunning benefits of modern handlebars.
In general, get your bike dialed. Get the handlebars and seat in the right place, as well as making sure your brakes operate without quickly locking. See our section on fitting your bike, an element more important than the bike itself.
Get a Quality Saddle
If your bike has a fat mattress saddle, replace it immediately with a quality racing-style saddle. Not only are they more comfortable, but they reduce thigh friction and allow you to move around for different riding conditions; forward for climbing hills, for example. Avoid useless gimmicks like "gel" covers and visible springs which prey on an ignorant consumer. For details, see our page on the horrors of soft saddles.
For women, choosing a saddle is more of an art. Avoiding unisex models in favour of a saddle designed specifically for women is a very good idea, as there are a lot of crap seats around, including many "women's" models that are actually just men's saddles, painted pink. Saddles are a major element of comfort and a very individual choice, so quality testing is a must. Detailed information on women's saddles will help you find the perfect saddle on the first try, found in the women's cycling section.
Get a Quality Bike
Bikes are expensive, just like cars are. While it is possible to buy a decrepit Chevette hatchback for $300, you can also buy a similarly-made bike at the local discount store for $149.95. However, a bike with acceptable components which will stay in adjustment, be well-designed and a pleasure to ride will start at about $400. If you don't have enough money to get a decent bike, then save. The $250 you spend at Wall-Mart will go down the toilet when you have to replace it in a couple years having learned the hard way. If you have the money, a $2,000 racing bike is worth it, for they are an unmatched pleasure to ride and last a lifetime.
Platform pedals are not to be used. You can't apply power for most of the pedal stroke, you're limited to a single set of leg muscles, your feet aren't automatically placed properly on the pedal, you can't hop over obstacles, and it's really cheap to fix the situation.
Toe clips are a great improvement. You can still use any shoes, and with less danger of damaging them than with platform pedals. If you want to cut your commute time, getting real pedals is second only to getting a real road bike in making your life easier. Toe clips are only about $5, while click-in pedals and cycling shoes will run $50-100 each for a solid pair. The main advantage of toe clips is that you can still ride to work in the shoes you plan to wear.
If you have stiff-soled cycling shoes, then you might as well get some clipless pedals to interface with them. You don't have to buy anything fancy, but the addition of proper cycling shoes and click-in pedals improve pedalling efficiency by as much as 25% over riding in soft-sole shoes with toe clips. (The actual gains depend a lot on what kind of shoes you were riding in before; sometimes I wonder if they're comparing click-in cleats to riding in slippers.) You have to wear funny cycling shoes, the stiff soles on which makes you walk like a penguin. You'll have to either stash a pair of work shoes or two at your destination, or carry them, which is a bit of a pain. But if you're change your clothes anyway, it's probably worth it.
Read more about different types of pedals.
Use Road Gearing, Not Alpine Gearing
A no-brainer in the same vein as getting a road bike if you ride on the road, don't get alpine gearing for a commuting bike. Road bikes come in a variety of gearing set-ups, so get one which is designed for efficient pedalling on roads and moderate hills, not climbing mud trails in the Andes. You will still have no problem getting up even the steepest hills: upright hybrid-beach-cruisers and cheap mountain bikes have the easy gears because they cripple your body's power output. With a bike that is properly set up, such as a well-adjusted road bike, you simply do not need them.
Make It Safe
Get a rear LED blinker for your bike, preferably a high-end model which is visible for 180 degrees. Use this even in daylight, especially during rush hour commuting times. They're only about $10, and are visible for about a kilometer. Rear collisions account for only a small fraction of collisions; the main reasons to use a blinker are psychological -- cars pass with more distance, and the rider is put at ease.
Wear both gloves and a helmet, and a mirror mounted on the helmet, bars, or sunglasses aren't a bad idea either. Some 88% of head injuries could have been prevented with a helmet, if properly adjusted as to protect the forehead. We have an entire section on Helmet Safety with lots of really interesting information.
Use quality brakes, quality pads, and learn to brake effectively. Most bike accidents involve a rider slamming into something (such as an opening car door, which is another story).