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Many countries have rules or regulations that specify what color your lights (headlights or rear lights) or reflectors must be. What are they?
In your answer, please note the country (and state, if applicable) and link to the regulations if possible.
Related: Reflective tape instead of rear reflector (Queensland, Australia)
New Zealand
Legal requirements for your bike:
Your responsibilities
It’s up to you (the rider) to:
If you don’t, you could get an infringement fine or be taken to court.
What are the ‘hours of darkness’?
Legally, ‘hours of darkness’ means:
That's all from the accessible "fact sheet" http://www.nzta.govt.nz/assets/resources/factsheets/01/docs/01-cycles.pdf dated February 2014.
Note the onus is on the rider of the bike to make sure its legal, not the owner should that be different.
Japan: Lights and Reflectors
Surprisingly, Japan's requirements for safety equipment are very lax only requiring a brake and a bell to be installed for daytime use. According to this summary, bicycles in Japan are required to have a front light and a single rear reflector only when operated at night or in dark tunnels. Front reflectors, pedal reflectors, and wheel reflectors are entirely optional.
The light requirement seems vague to me and requires someone with better Japanese language skills but it appears there is no requirement for headlights or tail lights to be installed on the bicycle itself. As long as there is a light (a headlamp, for example; or a red LED on your backback) that is shining at nighttime, you are ok:
ライト（前照灯・尾灯）は装備義務がない
夜間の道路等、前述の場所を通行する際には、ライト（前照灯、反射器材を装備していない場合には加えて尾灯）を点灯しなければならないが、これらについては、装備義務までは法律に定められていない。 そのため、適切に点灯することができるのであれば、例えば前照灯にはヘッドライトを用い、尾灯にはリュック等に付けた赤色LED灯を用いるなどしても、法律上は差し支えない。
You must, however, have an orange or red tail reflector at night that is visible if a car shines its high beams at you from 100 meters away:
反射器材の基準
反射器材は、次の基準を満たすものでなければならない。
性能： 夜間、後方100mから自動車の前照灯（ハイビーム）で照らし、反射光を容易に確認できること
色： 橙色または赤色
USA (CPSC) for reflectors (at point of sale):
The CPSC as coded in the Federal Regulations (§1512.16) says that the bike must have reflectors at the point of sale (when the bike is sold as new):
(a) Front, rear, and pedal reflectors. There shall be an essentially colorless front-facing reflector, essentially colorless or amber pedal reflectors, and a red rear-facing reflector.
(b) Side reflectors. There shall be retroreflective tire sidewalls or, alternatively, reflectors mounted on the spokes of each wheel, or, for non-caliper rim brake bicycles, retroreflective wheel rims. The center of spoke-mounted reflectors shall be within 76 mm (3.0 in.) of the inside of the rim. Side reflective devices shall be visible on each side of the wheel.
(c) Front reflector. The reflector or mount shall not contact the ground plane when the bicycle is resting on that plane in any orientation. The optical axis of the reflector shall be directed forward within 5° of the horizontal-vertical alignment of the bicycle when the wheels are tracking in a straight line, as defined in §1512.18(m)(2). The reflectors and/or mounts shall incorporate a distinct, preferred assembly method that shall insure that the reflector meets the optical requirements of this paragraph (c) when the reflector is attached to the bicycle. The front reflector shall be tested in accordance with the reflector mount and alignment test, §1512.18(m).
(d) Rear reflector. The reflector or mount shall not contact the ground plane when the bicycle is resting on that plane in any orientation. The reflector shall be mounted such that it is to the rear of the seat mast with the top of the reflector at least 76 mm (3.0 in) below the point on the seat surface that is intersected by the line of the seat post. The optical axis of the reflector shall be directed rearward within 5° of the horizontal-vertical alignment of the bicycle when the wheels are traveling in a straight line, as defined in §1512.18(m)(2). The reflectors and/or mounts shall incorporate a distinct, preferred assembly method that shall insure that the reflector meets the optical requirements of this paragraph (d) when the reflector is attached to the bicycle. The rear reflector shall be tested in accordance with the reflector mount and alignment test, §1512.18(m).
(e) Pedal reflectors. Each pedal shall have reflectors located on the front and rear surfaces of the pedal. The reflector elements may be either integral with the construction of the pedal or mechanically attached, but shall be sufficiently recessed from the edge of the pedal, or of the reflector housing, to prevent contact of the reflector element with a flat surface placed in contact with the edge of the pedal.
(f) Side reflectors. Reflectors affixed to the wheel spokes shall be mounted either flat on the spokes or within the spoke cage such that the angle between the optical axis and the normal to the plane of the wheel shall not exceed the angle of the spokes with the plane of the wheel. The reflectors shall not interfere with any wheel adjustments. The side-mounted reflector devices shall be essentially colorless or amber on the front wheel and essentially colorless or red on the rear wheel.
(g) Reflector tests. The pedal, front-mount, rear-mount, and side-mount reflectors shall be tested in accordance with the reflector test, §1512.18(n), to assure the reflectance values over the angles given in tables 1 and 2.
(h) Retroreflective tire sidewalls. When retroreflective tire sidewalls are used in lieu of spoke-mounted reflectors, the reflecting material shall meet the following requirements:
(1) The retroreflective material shall form a continuous circle on the sidewall.
(2) The retroreflective material shall adhere to the tire such that after the tire has been subjected to a temperature of 50° ±3 °C (122° ±5.4 °F) for 30 minutes, the retroreflective material cannot be peeled or scraped away without removal of tire material.
(3) The retroreflective material shall be as resistant to abrasion as is the adjacent sidewall material so that when retroreflective material is removed from the inflated tire by abrasion with a wet, steel bristle brush, tire material will be removed along with the retroreflective material.
(4) The retroreflective material shall be tested for performance in accordance with the retroreflective tire test, §1512.18(o), to assure the reflectance properties over the angles given in table 3. When a portion of the retroreflective material is selected (and the remainder is masked as specified in §1512.18(o)(2)(i)), the selected portion shall not contact the ground plane when the assembled bicycle is resting on that plane in any orientation.
(i) Retroreflective rims. When retroreflective rims are used in lieu of spoke-mounted reflectors or retroreflective tire sidewalls, the reflecting material shall meet the following requirements:
(1) The retroreflective material shall form a continuous circle on the rim.
(2) If the retroreflective material is applied to the rim in the form of a self-adhesive tape, the following requirement must be met: Use a sharp knife, razor blade, or similar instrument to carefully release an end of the tape material sufficient to be grasped between the thumb and finger. Grasp the freed tape end and gradually pull in a direction 90° to the plane of the rim. The tape material must break before additional separation (peeling) from the rim is observed.
(3) After the retroreflective material is abraded in accordance with the abrasion test for retroreflective rims at §1512.18(r), the rim must then be tested for performance in accordance with the retroreflective tire and rim test at §1512.18(o), to assure the reflectance properties over the angles given in table 3.
[43 FR 60034, Dec. 22, 1978, as amended at 45 FR 82627, 82628, Dec. 16, 1980]
As Daniel Hicks and Punctual Emoticon note, the CPSC / Federal regulations are for bikes that are for sale. Each individual state has rules that govern bikes that are on the road. These should be separate answers.
Some of these rules can be ignored for road bikes, as the fitting spaces are not available, but the police can choose to fine you if they find your bike not up to the required standards
Sources:
Minnesota Statutes section 169.222 OPERATION OF BICYCLE
Subd. 6.Bicycle equipment.
(a) No person shall operate a bicycle at nighttime unless the bicycle or its operator is equipped with (1) a lamp which emits a white light visible from a distance of at least 500 feet to the front; and (2) a red reflector of a type approved by the Department of Public Safety which is visible from all distances from 100 feet to 600 feet to the rear when directly in front of lawful lower beams of headlamps on a motor vehicle. A bicycle equipped with lamps that are visible from a distance of at least 500 feet from both the front and the rear is deemed to fully comply with this paragraph.
(b) No person may operate a bicycle at any time when there is not sufficient light to render persons and vehicles on the highway clearly discernible at a distance of 500 feet ahead unless the bicycle or its operator is equipped with reflective surfaces that shall be visible during the hours of darkness from 600 feet when viewed in front of lawful lower beams of headlamps on a motor vehicle. The reflective surfaces shall include reflective materials on each side of each pedal to indicate their presence from the front or the rear and with a minimum of 20 square inches of reflective material on each side of the bicycle or its operator. Any bicycle equipped with side reflectors as required by regulations for new bicycles prescribed by the United States Consumer Product Safety Commission shall be considered to meet the requirements for side reflectorization contained in this subdivision.
(c) A bicycle may be equipped with a front lamp that emits a white flashing signal, or a rear lamp that emits a red flashing signal, or both.
...
Subd. 7.Sale with reflectors and other equipment.
(a) No person shall sell or offer for sale any new bicycle unless it is equipped with reflectors and other equipment as required by subdivision 6, paragraphs (b) and (e) and by applicable regulations for new bicycles prescribed by the United States Consumer Product Safety Commission.
(b) Notwithstanding paragraph (a), a new bicycle may be sold or offered for sale without pedals if the bicycle otherwise meets the requirements of paragraph (a).
Poland
bike - a vehicle up to 0.9 m width, up to 4.0m length, powered by the rider's muscles; bicycle can be equipped with a pressure activated pedal auxiliary electric drive supply of voltage not higher than 48 V with a rated continuous power of 250 W, the output power gradually decreases and drops to zero at speeds above 25 km / h; "bicycle trolley" - the same as above, with width more than 0.9 m
bicycle must be equipped with:
All this lights should be mounted no lower than 250mm and no higher than 1500mm above the groung. Passive reflector, lit with another vehicle's high beam, and all lights should be visible at night with good clarity of air from a distance of at least 150 m. Except rear red passive reflector, all lights can be dismounted when not required (eg. during the day)
List of the rest of obligatory equipment:
Optional equipment
Source: official regulation, extract with comment
USA - California: Lights and reflectors
The road legal code in California is as follows:
(d) A bicycle operated during darkness upon a highway, a sidewalk where bicycle operation is not prohibited by the local jurisdiction, or a bikeway, as defined in Section 890.4 of the Streets and Highways Code, shall be equipped with all of the following: (1) A lamp emitting a white light that, while the bicycle is in motion, illuminates the highway, sidewalk, or bikeway in front of the bicyclist and is visible from a distance of 300 feet in front and from the sides of the bicycle. (2) A red reflector or a solid or flashing red light with a built-in reflector on the rear that shall be visible from a distance of 500 feet to the rear when directly in front of lawful upper beams of headlamps on a motor vehicle. (3) A white or yellow reflector on each pedal, shoe, or ankle visible from the front and rear of the bicycle from a distance of 200 feet. (4) A white or yellow reflector on each side forward of the center of the bicycle, and a white or red reflector on each side to the rear of the center of the bicycle, except that bicycles that are equipped with reflectorized tires on the front and the rear need not be equipped with these side reflectors. The reflectors and reflectorized tires shall be of a type meeting requirements established by the department. (e) A lamp or lamp combination, emitting a white light, attached to the operator and visible from a distance of 300 feet in front and from the sides of the bicycle, may be used in lieu of the lamp required by paragraph (1) of subdivision (d). (Amended by Stats. 2015, Ch. 549, Sec. 2. Effective January 1, 2016.)
Headlights are required after dark. What's interesting about this is that the headlight must be visible from 300 ft (~100 meters) from the front and from the sides. Many bike lights do not have side illumination, so they fail the code.
The taillight may be either a red reflector, a solid red light, or flashing red light.
And the legal code actually allows for headlamps, which is interesting.
And totally off-topic, the first clause is that "(a) No person shall operate a bicycle on a roadway unless it is equipped with a brake that will enable the operator to make one braked wheel skid on dry, level, clean pavement." which would make bicycle anti-lock brakes illegal! :-)
USA - Alabama - Nighttime Lighting and Reflectors
http://alisondb.legislature.state.al.us/alison/CodeOfAlabama/1975/32-5A-265.htm
Section 32-5A-265 Lamps and other equipment on bicycles.
(a) Every bicycle when in use at nighttime shall be equipped with a lamp on the front which shall emit a white light visible from a distance of at least 500 feet to the front and with a red reflector on the rear of a type approved by the department which shall be visible from all distances from 100 feet to 600 feet to the rear when directly in front of lawful lower beams of head lamps on a motor vehicle. A lamp emitting a red light visible from a distance of 500 feet to the rear may be used in addition to the red reflector.
(b) Every bicycle shall be equipped with a brake which will enable the operator to make the braked wheels skid on dry, level, clean pavement.
(Acts 1980, No. 80-434, p. 604, §12-107.)