Always be safe on the road. Do not be daring, do not insist on the right of way, do not break traffic laws (yes, you have to follow them too), and always be as visible as possible. If you know the common causes of accidents, you can look out for them:
Opening car doors. This is a common one — someone opens their car door, right into your path, and you don’t have time to swerve. Slam! The only thing to say is to be on the lookout for any doors that are about to open, and don’t ride too close to parked cars.
Sideswiped. If you right on the outermost edge of the road, as many cyclists do, cars will be tempted to try to pass you in the same lane. As this is a tight fit, this could result in you being hit. It’s safest to take the center of the lane, even if that doesn’t seem as safe, until you can safely move to the shoulder to let cars pass if necessary. You have just as much a right to that lane as the cars do.
Intersections. If you are making a left turn across an intersection, be very careful. You might think that the oncoming traffic, or the cross traffic from either side, will see you, but you could be wrong. Be very sure you are seen by all drivers. Right turns can also be dangerous if the traffic going into that lane doesn’t see you — or if the driver behind you also making a right turn doesn’t see you, as he is busy looking to his left.