Simple systems with a permanently lit pilot light
A permanently lit pilot light wastes gas, and needs user intervention to re-light it if it blows out or if the gas fails. However, it can be quite useful in a combination boiler, as it keeps the water warmish, thus reducing the delay in the production of hot water when it is required after a long period of standing.

The gas valve has a means of shutting off the pilot light, and the main burner, if the pilot should fail. The presence of the pilot light is sensed by a simple system: a thermocouple. A thermocouple is any junction of dissimilar metals. A small voltage is generated at the junction, proportional to its temperature. If the dissimilar-metal leads from a thermocouple are joined together, current will flow, but only if the two junctions are at different temperatures, because otherwise the voltages generated at each will cancel out.

In a gas boiler, the "hot" junction is in the pilot flame, and the "cold" junction is in the gas valve. Thus, if the pilot is lit, a current will flow round the circuit. This passes through an electromagnet, which holds the gas valve open. The current is far too small to pull in an electromagnet, so the clever bit is that the user does this by pressing in the button on the gas valve. There will also be some sort of interlock to prevent the main burner activating while the button is pressed in.

If the pilot is then lit (either with a match, a manual piezoelectric spark or an electronic spark generator), after a few seconds the hot junction will be hot enough for the electromagnet to hold the valve open against a spring. If the pilot goes out for any reason, after a few seconds the hot junction will cool and the electromagnet will release, closing the valve until it is manually opened again.

If there is an ignition system and it does not produce sparks, it may be faulty, its high tension connection to the electrode may be breaking down (the return path is always through the body of the boiler), or the electrodes may be too far apart (due to being interfered with or corroding away). If there are sparks and the pilot will not light, the electrode positioning or the pilot adjustment may be wrong, or the pilot jet may be blocked, resulting in no gas getting near the sparks. No gas can also result from a faulty gas valve, or air in the pipes. (With my old combi, the only way to re-light it was to fool it into thinking that the pilot was lit, and activate the main burner for a couple of seconds to purge air.)

The thermocouple is rather confusing in that it looks like a capillary, as used in thermostats. The hot junction is a probe which sits in the flame, and a thin flexible copper tube, acting as one conductor and containing the other, leads back to a fitting on the gas valve secured with a small back nut. Thermocouples do fail, and are cheap to replace at about a fiver, but before this is done it is worth making sure that the probe is correctly positioned in the flame, and the flame is the right size (as specified in the boiler manual). Pilot jets can get blocked, and there will be a pilot adjustment on the gas valve. Sometimes there is a deflector to direct part of the pilot flame towards the thermocouple, and part towards the main burner.

If the pilot flame is correctly adjusted but the gas valve will not stay open at all, the thermocouple (or the gas valve, but unlikely) is open or short circuited. Sometimes thermocouples may fail intermittently, leading to the confusing symptom of the boiler working for a while and then giving up, as the heat of the main burner causes the thermocouple to expire temporarily. However, this may also be caused by strong air currents due to heating by the main burner blowing out the pilot. The pilot needs to be watched, to see if it goes out before or just after the characteristic click of the gas valve releasing.