My roof is leaking, what could be the cause?

There are key reasons for a roof to leak: - 

Roofing Felt - one of the most common causes in older roofs is due to the failure of the underlay and battens. Whilst roof tiles and slates are designed to keep out the rain, it is still accepted that some wind driven rain will pass through. The purpose of the roofing underlay is to carry such water ingress away to the gutter. 
Most houses have been installed using bituminous roofing felt, which will succumb to rot over time. The rate that this occurs will depend on the amount of moisture present, which can come through the tiles but also from within the home. Houses that have had a change of use with new bathrooms added produce more moisture-laden air. If not adequately ventilated this will increase the rate of failure of the roof underlay.  Today most underlays are made from materials such as polypropylene and are far more durable
Roof Junctions - Another likely cause of a roof to leak is due to flashings at junctions being incorrectly installed or detailed; valleys are particularly vulnerable because water is directed towards these due to the geometry of the roof. Side abutments are also vulnerable if not correctly installed.  
Roof Windows - If your home has been built with roof windows, or they have been added later, this can be a further cause of leaks. It is very unlikely that the roof window itself is leaking. The problem usually comes from the flashings being incorrectly installed, or the roof light being installed below its minimum recommended pitch (which may be different from the surrounding tiles). 
Lean to extensions - If the water from main roof is allowed to discharge directly onto a smaller lower roof (usually an extension) then the sheer volume of water will be too much for the tiles or slates which is very likely to cause water ingress.  
Tiles and Slates - The actual tiles or slates are probably the least likely element of the roof to leak. If, however, you do think that water is leaking through the tiles, then ask a roofer to check the following: -
1.    They are laid at or above the minimum recommended roof pitch.
2.  The tiles are laid at the correct headlap
3.   The tiles may have been laid to the correct bond pattern (flat tiles are normally laid broken bond with profiled tiles laid straight bond)
Of course if a tile has slipped out of position this will be very easy to see and is relatively easy to fix by a professional. 
Roof ventilators - If you think that a ventilator is leaking, check that this is not actually condensation, rather than rainwater. This is very common in mechanical extract systems where the pipe running through the loft space has not been properly insulated all the way to the outside.
 
Condensation - it is not uncommon for suspected leaks to come from condensation within the home, rather than outside; if a roof space is not correctly ventilated then condensation may form on the underside of the felt or tiles and can, in severe cases form enough water to drip onto the ceiling, giving the impression of a leaky roof.