Weather: Beware of bad weather - it can be dangerous for cyclists. The wind can take you off track, rain can make the ground slippery and heat and cold can seriously dehydrate your hands and face! Take whetever you might need to protect yourself from the elements and keep abreast of the weather when you head out.
Light: Cycling at night isn't a good idea, especially if you're out in the country, unless you've got all the right equipment: front and back lights, flashing diode lights, reflective clothing and reflective bands.
Hazards and roadworks: Avoid road markings (they can be slippery) and tramway lines. If you have to go over cobbles, stop pedaling, move your weight backwards on your cycle and flex your legs to absorb the shock of bumps. If it's raining and the ground is slippy, take care when turning and braking.
Traffic: If there are cars around, keep a permanent eye on what's happening around you (hazard warning signs, sidestreets, etc) and always keep 2 or 3 fingers permanently on your brakes so that you can stop quickly. Look behind you often and before changing direction, show people around you where you're going by signaling with your arm. Always keep your distance from other vehicles.