+1

I won't leave home without it.

Depends on your commute.
For me it is 14 rural miles at night.

A comfortable, lightly loaded backpack for windbreaker and wind pants, couple of granola bars ect.
Bike rack with trunk pack in case I need to pick up a few grocery items.
Cable and U locks. I leave these at work so I don't have to lug them around.
Fenders.
Basic tools.
Spare tube and patch kit.
Tire pump.
Very bright headlight (tactical flashlight on the handlebars in adjustable homemade mount) and taillight that uses the same batteries (AAA rechargable) .
3 spare AAA batteries (lithium primary).
Strap on LED headlight for backup light.
Waterbottle.
Cell phone.
No flames please but I always wear a helmet.

I'm assuming the bike itself has everything it needs (comfortable saddle, working gears, etc.)

I like to keep stuff to change a flat on my bike. This includes a hand pump along with a tube, patch kit, and a boot.
Lights are a given. With the time change, you'll start riding in dark more or when the sun sets.
I think reflective tape is overlooked. I think it's need just as much as lights are.

A rack is nice, but not needed. It helps keep sweat off my back and allows me to be more free while riding.
Of course a water bottle/thermos bottle holder.

Decent tires. If you're commuting to work or school you can't afford to be late. I like to get tires that have some flat protection so I won't get as many flats.

I also have an AirZounds horn on my commuter.

Lastly, a good lock. If this is a bike you're going to be riding five days a week, invest in a good U lock and possible a cable lock.

----

For the bar essentials. All you need is stuff to change a flat. Lights too, unless you commute during the day.

No-one has mentioned gloves. If you take a spill at low speed you may get a bit banged up and grazed but nothing serious BUT if you slide your hands along the tarmac you are out of action for months.

I took 1mm of leather off my gloves in a crash and was back at work by mid-day.

I have gone back and forth on this.
Today's rig:

Front and back lights (the tiny strong kind)
Reflectors on the spokes
Bottle and cage
Bike lock (Just a cable kind, lighter but not for overnight or dark alleys)
Small under seat bag for ID, $$, First aid kit and room for my cell phone if it rains.

No tools, no tire repair stuff. (I am terrible at tire changing, so I just call a buddy)
Took off racks, fenders and kickstand.

Isn't that why we're here?

While I don't disagree with your logic (I own both types), I would say if you're just starting out, buy the Road Morph first - It isn't quite as easy or capable as a floor pump, but it is sufficient to get my road bike tires up to 120psi, while being MUCH easier to carry with me than my floor pump. Honestly, if I hadn't already owned a floor pump, I might have just made do with the Road Morph. I gave my cheap mini pump to my daughter for college ;-)

Best advice. The other things only help... they won't get you out of bed in the winter and on the bike.

I've got all of these as well, except the horn.

I've given a cursory look at some of the other lists and they look pretty good but FWIW here's mine for a 21 mile round trip in the Boston area.

Bike:
Solid and simple. (mine's a 9 speed REI Buzz all black matte finish).
Brooks B15 saddle
Racks front and rear.
2 bungee cords
Milk crate back.
2 front lights- handlebar mounted.
1 helmet light
rear light mounted on rack
1 blinkie attachable to clothing/helmet/bike
bell
Performance "campus" pedals (clipless one side, platform other)

"Stuff"
Messenger bag (throw it in milk crate or sling on shoulder as needed)
carries rain gear
extra clothes
extra batteries for lights
cell-phone
and
Tools:
mini-pump
spare tube
patch kit
bike multi-tool
tire levers (METAL- plastic breaks in winter)
small "leatherman"- I like having the pliers


Clothes:
Helmet
Showers Pass rain jacket- I carry it only when rain threatens
Rain pants " " " "
Shoe covers- only use in cold, wet, weather
Keen cycling shoes
Gore Wind Stopper Vest by Mountain Hard wear- use it or carry it almost all the time (except mid-summer)
Gloves- cycling gloves- often but not everyday, winter thin layer gloves, then thicker gloves then Gore-tex mitten shell for cold wet winter.
Layers, layers, layers.

wow, thanks for all the replies. This is pretty helpful.

-Peter

Other stuff or variations that I carry:
-I buy those cheap plastic rain coats that weigh almost nothing and carry one. Almost like saran wrap... They take almost no space and give me some protection should I want.
-Also a single bungee wrapped over the bike rack. I got some with five straps between two hooks. Spread 'em if you need 'em.
-Small bottle (sample size) of waterless hand cleaner. You never know...
-Small cable ties about a dozen. Weigh nothing and can even be put together to make a longer strap.
-Medicine: Sugar tabs (I am diabetic) and prednisone which I need for another medical issue and its ensuing unexpected crises.
-Food. Either a Clif bar or a few fig bars.

+1

Like many have said, it depends on your commute. You probably want your travel to be Safe, Reliable, Enjoyable. I mostly cary stuff others have mentioned.

One thing I keep in my bike bag is bus fare. Haven't needed it yet, but it's always there. I also have a pencil and a couple of note cards. Pencils tend to last better than most types of pen.

About 9 miles each way. Rarely, maybe never more than twice per week.

It's fun to ride long distances, even if just for the day. You get to see places you would have missed with the car; try it, but work up to it.

I carry other stuff too, I just listed the basics. I carry $40 cash, State and insurance ID, spare bats for the flashers, SuperGlue, small first aid kit, pills for headaches and diarrhea, house key. On long rides of over 40 miles from home I take a handlebar bag and put some food in and a rain jacket and helmet rain cover, and depending where I'm going I may take some other things.