Mandatory equipment of bicycles in the Czech Republic

If you want to ride your bike on public roads and streets here, it must have:

Brakes. At least two, independent, powerful enough and with a possibility to regulate the braking power (so a parking brake that can only lock a wheel doesn't count).
Reflectors. Minimum is one white at the front, red at the rear, yellow somewhere between spokes (visible from the side) and yellow on the pedals. All of them can be replaced by reflective materials or stickers on tyres, shoes, clothes etc., so with a hi-vis vest and ankle bands, you can legally ride a bare frame if you want to.
Lights during low visibility conditions. White light at the front (aiming max. 20 m far before the bike to avoid glaring), or at least a white blinky if you only ride on well-lit streets. Red light or blinky at the rear. If the lights run on batteries, they must have capacity for at least one and half hour.
No dangerous sharp things. Tube ends should be plugged, levers should be rounded or rubber-coated, axle ends shouldn't stick out through the nuts etc.
Wheels in good condition. No cracked rims, no "taco" shapes etc.
Children under 18 years must wear a helmet.

Years ago, bell and mudguards were mandatory too. Today they are not, but that doesn't mean they are not handy. A bell clearly tells people that a bike is approaching. If I hear someone shout, I suppose he is walking and I have plenty of time for evasive maneuvers. A car horn, on the other hand, suggests something fast and motorized, so I jump into a ditch first and look around later. Ship horns or locomotive whistles don't bother me at all - a ship on a cyclepath? Concluded: volume alone is not everything.

Bikes and other human-powered vehicles don't need any registration or license plate and you don't need a driver's license to ride them. It's also OK to ride homebuilt machines, as long as they meet the requirements above.

One more remark for the lights. Please please really keep your headlight aimed slightly down and don't dazzle oncoming people. Truck drivers may not mind much, but a cyclist (especially out of town) can't see a thing if he gets hit between his eyes by a photon gun.

Full wording of the rules and laws can be found in vyhláška 341/2014 and zákon 361/2000 (Czech only).