This would normally be oil being burnt in the combustion chamber due to engine wear; however there are a couple of things which can also cause the problem.
1. Breather Blocked
First check that the engine breathers/pipes are clear and not blocked this can blow oil into the air filter/pipes.
2. Turbo Charger
If it has suddenly happened and the vehicle is turbo charged it could be that the turbo oil seals have failed this will pump large amounts of oil into the intake manifold.
3. Engine Worn
Depending on how bad the problem is it could be valve stem oil seals, this would normally be worse in the morning after the oil had seep pass the seals and down the valve stems, the repair would normally require cylinder head removal. The second problem would be worn pistons, this would create excessive amounts of crankcase back pressure this would be evident out of the breathers and dipstick tube, in a very worn engine it will look like a steam engine puffing, the engine will be using excessive amounts of oil and there would be deposits of carbon on the spark plugs. A compression test will normally show if the pistons are worn and a full rebuild is required.
Contaminated fuel (petrol in diesel) can also produce blue smoke but this is normally associated with loss of power at the same time.
Black smoke is un-burnt fuel, on an old petrol car this would be choke stuck on or blocked air filter, but with lambda sensors monitoring emission, the ECU will adjust the mixture to compensate for a problem but will put engine management light on if a large trim is required.
On a diesel vehicle it is normally caused by the EGR valve sticking open (see EGR page), to much exhaust gas prevents complete combustion due to lack of oxygen. High mileage diesels with worn injectors will also give bad combustion and black smoke.
White smoke with a warm engine would normally be the head gasket allowing coolant to enter the combustion chamber and turn to steam. (See over heating)