See the links below for cycling related laws in Washington. This is not intended to be a comprehensive list. Please keep in mind that these laws are constantly changing.
State of Washington
Definitions:
RCW 46.04.071 - Bicycle.
RCW 46.04.197 - Highway.
RCW 46.04.200 - Hours of darkness.
RCW 46.04.400 - Pedestrian.
RCW 46.04.500 - Roadway.
RCW 46.04.670 - Vehicle.
Traffic Laws:
RCW 46.61.755 - Traffic laws apply to persons riding bicycles.
RCW 46.61.770 - Riding on roadways and bicycle paths.
RCW 46.61.526 - Negligent driving -- Second degree -- Vulnerable user victim -- Penalties -- Definitions.
RCW 46.61.050 - Obedience to and required traffic control devices.
RCW 46.61.115 - When overtaking on the right is permitted.
RCW 46.61.160 - Restrictions on limited-access highway -- Use by bicyclists.
RCW 46.61.235 - Crosswalks.
RCW 46.61.261 - Sidewalks, crosswalks -- Pedestrians, bicycles.
RCW 46.61.305 - When signals required -- Improper use prohibited.
RCW 46.61.620 - Opening and closing vehicle doors.
RCW 46.61.750 - Effect of regulations -- Penalty.
RCW 46.61.758 - Hand signals.
RCW 46.61.760 - Riding on bicycles.
RCW 46.61.765 - Clinging to vehicles.
RCW 46.61.775 - Carrying articles.
RCW 46.61.780 - Lamps and other equipment on bicycles.
RCW 46.61.790 - Intoxicated bicyclists.
RCW 47.30.070 - Bicycle, equestrian, pedestrian paths as public highways.
Traffic Safety Commission:
RCW 43.59.010 - Purpose -- Finding.
Driver's Education Bicycle Safety Requirements:
RCW 28A.220.085 - Information on driving safely among bicyclists and pedestrians.
RCW 46.20.093 - Bicycle safety.
RCW 46.82.420 - Basic minimum required curriculum -- Revocation of license for failure to teach.
City of Seattle
Definitions:
SMC 11.14.055 - Bicycle and Electric-assisted bicycle.
SMC 11.14.060 - Bicycle lane.
SMC 11.14.310 - Marked bicycle crossing.
SMC 11.14.525 - Right-of-way.
SMC 11.14.710 - Vehicle.
Bicycle Rules:
SMC 11.44.010 - Where regulations apply.
SMC 11.44.020 - Rights and duties of rider.
SMC 11.44.040 - Riding on roadways.
SMC 11.44.060 - Riding more than two (2) abreast prohibited.
SMC 11.44.080 - Overtaking and passing on right.
SMC 11.44.100 - Right-of-way in crosswalk.
SMC 11.44.120 - Riding on sidewalk or public path.
SMC 11.44.140 - Hand signals.
SMC 11.44.160 - Lamps and reflectors on bicycles.
SMC 11.44.200 - Brakes.
SMC 11.44.210 - Must ride on seat.
SMC 11.44.220 - Passengers.
SMC 11.44.240 - Clinging to vehicles.
SMC 11.44.260 - Control.
SMC 11.44.280 - Parking.
SMC 11.44.320 - Responsibility.
Miscellaneous Rules:
SMC 11.58.050 - Opening and closing vehicle doors.
SMC 11.58.310 - Regard for pedestrians.
SMC 11.52.020 - General speed stated.
SMC 11.53.190 - Driving in a bicycle lane.
SMC 11.53.195 - Marked bicycle crossing.
SMC 11.53.200 - Overtaking other traffic on the left.
SMC 11.53.340 - Overtaking on right upon multiple lane street.
SMC 11.53.380 - When conditions safe.
City of Bellevue
BCC 11.60.070 - Riding on sidewalk - General criteria.
BCC 11.60.080 - Right-of-way on sidewalk - Overtaking and passing.
BCC 11.60.090 - Bicycle helmets.
BCC 11.60.120 - Violations - Responsibility of parent.
BCC 11.48.140 - Emerging from an alley or driveway.
BCC 3.43.310 - Use of nonmotorized vehicles - Prohibited in certain areas.
City of Tacoma
Tacoma's bicycle-related traffic laws are found in the document linked below. You must scroll down to Chapter 30 to find the pertinent bicycling statutes.
Tacoma Municipal Code Title 11 - Traffic
TMC 11.30.010 - Purpose and policy.
TMC 11.30.020 - Definitions.
TMC 11.30.030 - Helmet required.
TMC 11.30.040 - Bicycle, skateboard, roller skate, scooter races, and events - Helmet required.
TMC 11.30.050 - Bicycle, skateboard, roller stakes, and scooter leasing or loan - Helmet required.
TMC 11.30.060 - Helmet sales - Safety standards.
TMC 11.30.070 - Penalties - Civil nontraffic violations.
TMC 11.30.080 - Enforcement.
TMC 11.30.090 - Information and education.
King County
Board of Health Code:
KCBOHC Title 9 - Bicycle Helmets.
County Code:
Rules for use of facilities. Visit KCC Chapter 7.12 and scroll down to KCC 7.12.295 for the King County Code provision regarding bicycle trail use.