The top of my radiator is cold but warm at the bottom: That means rust and sludge has built up at the bottom of the radiator – displacing water – which leaves the bottom of the radiator cold.
Proprietary sludge removers can be used to clean systems through. Theses are on sale at most plumbers merchants but in many cases it might be wise to ask a central heating specialist.
My downstairs radiators are hot but my upstairs ones are cold: You probably have a feed and expansion tank in your loft that has run dry – meaning there is a problem with the valve.
Although this is not a huge job and, as long as you have turned off the water, is well within the capabilities of a DIY enthusiast.
Upstairs radiators hot, downstairs cold: This might mean a faulty central heating pump. Only a trained engineer can fix this.
All my radiators are lukewarm: Similarly to the bottom being cold, rust and sludge has probably built up and you might need sludge cleaning materials.
My radiators are warmer nearer the boiler: Your central heating system needs balancing. Turn the valves down on the radiators nearest the boilers to restrict the flow to them and allow those furthest away a greater share of the hot water.