No lights
Usually the fault lies with the wiring, not the dynamo. Just as with any other lighting setup a methodical search helps. Disconnect the rear light first, if the headlight now works normally, you have probably swapped the leads to the rearlight causing a short.. 
If this doesn't work remove the leads from the dynamo. Give the wheel a spin and shortcircuit the terminals with a coin or key. If you get sparks and the wheels slows down measurably the hub is ok. 
Reconnect the wiring and spin the wheel again. If flipping the switch doesn't do anything you have an open circuit (look for blown bulbs or broken connectors), if the wheel slows down as short circuited on one or both positions of the switch you again have a short circuit (incorrect wiring, frayed cables).
If the dynamo fails to deliver current (easily checked by giving the wheel a spin and shortcircuiting the terminals with a screwdriver: sparks should be visible) the internal wiring in the dynamo could be faulty. This can be damaged if some moron er.. ill advised individual tries to adjust the non-adjustable bearings, or by riding around with a loose skewer. This is has to be repaired by a SON approved technician (eg the importer of factory)

E6

Most frequent mistake is putting the black switchring back on reversed. The magnet won't reach the reedswitch and the light will remain dark.
With the E6 it is possible for the central contact-spring to short circuit against the spring holding the bulb in place in the reflector. My guess is this can happen when the bulb slips out of the reflector during insertion. Carefully bend the spring back with a ballpoint refill or similar.

No front light (classic round Lumotec only):
The contact-lip (which contacts the back of the bulb) could be bent backwards. This can happen if you reposition the light frequently with the mounting screw done up tight. To fix open the Lumotec, remove the coil spring, bend  the central contact forward a few millimeters and reassamble. Stop readjusting the angle of the light, or loosen the screw first.

Dim frontlight
Bulbs only have a lifespan of around 100 hours (a household bulb = 2000-3000hrs!) With age the filament windings could weld together and short out, which decreases the light emitting surface. Replace the bulb for full power.

No rear light 
The Son has no connection to earth. If you use single wiring to the rear light the returnpath is made up by the connection through the frame to the front light. Ensure that both components are securely connected to the frame.

No front and rear light
Lights usually have a connection to earth. If you use double wiring to connect the rear light to the front, do not get the wires mixed up. If you connect the wires crosswise, the dynamo will be shortcircuited.

Frequent front bulb failure.
Mean time to failure for a bulb is around 100 hrs, and even less (30-50) for the fast crowd. If you ride a lot that could mean several bulbs a year. If the bulbs fail a lot sooner, a failed or disconnected Z-diode is usually the culprit. With old Lumotecs the diode sometimes makes poor contact, with the Lumotec Senso the diode could melt its connection to the circuitboard.
If you use a headlight only, without connecting a rear light, change the bulb to one rated 3 watts.
Fitting the headlight to the unsuspended part of a suspensionfork is very hard on the filament and will shorten bulblife.

Irregular & spotted beam
This is usually caused by faults of the filament. With old bulbs the winding could have shortcircuited, causing irregular lighting. With cheap bulbs the filamentposition could be out of specification, moving the light source out of focus

The properly defined filament is on the left, the 'cheap' bulb is on the right. Note the much more widely spaced filament windings

Rear light bulb failure
This is usually caused by the high voltage caused by a failed frontlight together with a dis-functioning Z-diode. Check the headlight if this happens.

Rear light goes on late or not at all
A frontbulb with shortened windings has a lower resistance, causing the voltage to drop (the Dynamo is a currentsource) If the voltage is too low LED lights with standlight will not function well. Replace the front bulb to restore light at both ends
 

Noisy hubdynamo

Bearing play
Newly installed bearings have zero play. With use the axial and radial play could increase to 0.01-0.02mm. This will result in approx. 0.2 mm sideplay at the rimface. This cannot be adjusted out and is normal for this kind of bearing. If you find a lot more play the bearings are probably damaged and you should return the hub for service. Never try to adjust the bearings, you'll only succeed in severing the electrical connections and voiding the guarantee!

Rattling noises
These are usually caused by an unsufficiently tightened skewer. Check that the OLD of the fork is 100 mm (XS excepted), and that the dropouts are parallel and that the skewer is really tight

Irregular grinding noises
This could be caused by sand in the labirinth seal, or a fragment of the very brittle magnets running around in the hub. This isn't critical and should disappear with use. 

Regular grinding noises, difficult turning or locked axle.
This could be caused by a locked dynamo, not by bearing failure. The interior is well sealed. If -salt-water manages to find it's way inside, it won't come out easily. Thus the hub could freeze solid, or rust particles could get jammed in the narrow crevice between stator and rotor. Do not keep riding this dynamo but send it in for service.

SON's old type (with black centersection prior to '99)
We have never imported this type which needs to be unspoked from the wheel before it can be serviced. Son guaranteed the hub for three years after purchase, but it can be sent in just like the others for service.
This also applies to the hubgenerators Wing 1,2 en 3 by Union and Marwi: these are based on a design by and can also be repaired by Schmidt.