Protect your number one asset! I wasn't born rich or good looking -- so my brain is my strong point, although some would argue this. Be that as it may, I'd wear a helmet if I rode a bike. Even minor bumps can cause spills resulting in head impacts and at as little as 4 mph, a head injury can be fatal. One estimate says that as high as 85% of these injuries could be prevented by helmets.
Especially in low-light or at nighttime, a bicyclist is hard to see. I've seen bike riders with no lights, wearing black clothes, riding along in the half-light of dusk, with no clue that they are virtually invisible. Wear bright, reflective clothing or light colors. Use reflective tape; put reflectors and lights on your bike. Battery-powered, pulsating "strobe" lights are especially good for "being seen." Be aware of where and when you are hard to see and ride to be visible. Don't ride where you are hidden by other vehicles or obstructions.
Remember the pedestrian you knock off the sidewalk today may be the motorist who sideswipes you tomorrow! Be courteous and respectful. When approaching pedestrians, reduce speed. Give them a polite verbal warning and a wide berth. Be courteous to motorists too. Use hand signals and be careful not to impede traffic. Obey all traffic laws when riding on the roadway. Remember that no matter the cause, if there is a collision, you lose.
Pay attention. Be aware of your surroundings and control distractions and impediments. You need all your senses when riding -- don't wear a headset stereo. Same with cell phones; it's dumb to ride a bike, watch traffic, and talk on a cell phone all at the same time.
Develop smart "road moves." Be predictable. Ride with the traffic, not against it. One of the top causes of bicyclist injury is riding the wrong way and being hit by a vehicle turning right - the driver doesn't look to the right, he's looking left for the chance to get into traffic. Chances are he never looks right until he hears the crash of a bicycle against his right front fender.
"Take the lane" when necessary for safety. Bikes should operate single-file, as close to the right curb as possible. But if the road is too narrow for a car to pass a bike safely within the lane, the bike should "take the lane" in the interest of his own safety (to prevent the motorist from passing unsafely). Do a head check, then move left a quarter or a third of the way into the lane until the road is wide enough to accommodate both the bike and the vehicle safely again. Do the same when there are road hazards. Watch for railroad tracks, debris, uneven road surfaces, loose gravel, and parked cars that are ready to pull out -- or open their doors. Be ready to swing wide when necessary, but make sure you "check six" (look behind you) first.
Finally, make safe left turns. Bikes can join the traffic to make left turns, but while legal, this can be a dangerous thing to do. Instead, why not continue straight across an intersection in the right lane, stop, get off your bike and use the crosswalk to cross the street, remount, and continue in the desired direction. However you do it, make sure you keep your eyes moving and beware of any impending dangers -- city intersections are dangerous and busy places, especially for a bike rider.
To summarize, protect your head, be visible, be courteous, and ride smart!