Excessive Hum

A good way to divide and conquer is to turn the volume control(s). If the hum changes levels as you do this, then the source of the hum is something that affects the stages of the amp before the volume control. A faulty, humming preamp tube can be isolated this way very quickly. Conversely, if the volume control does not affect the hum, the cause is somewhere after the volume control.

Faulty tube

Tubes sometimes develop internal hum, for reasons known only to themselves. Do some tube swapping to locate the problem. Use the volume control test

Severely unmatched output tubes in a push pull amplifier

Push pull amplifiers get by with less power supply filtering because they're supposed to cancel this ripple in the output transformer. The cancellation can be upset by output tubes that use different amounts of bias current, allowing the hum to be heard.

Faulty power supply filter caps

Faulty bias supply in fixed bias amplifiers

A bias supply with excessive ripple injects hum directly into the grids of the output tubes. Check that the bias supply diode is not shorted or leaky, and then bridge the bias capacitor with another one of equal value to see if the hum goes away.

Unbalanced or not-ground-referenced filament winding

Defective input jack

If the input jack is not making good contact to the guitar cord shield, it'll hum. Likewise, if the jack has a broken or poorly soldered ground wire, or not-very-good connection to the grounded chassis, it will cause hum. If messing with the jack changes the hum, suspect this.

Poor AC grounding

In amps with two wire cords, defects of the "ground reverse" switch and/or capacitor can cause hum. A leaky power transformer can also cause this. It's especially bad when the ground reverse mess is already dicey.

Induced hum

Placement of the amplifier near other equipment can sometimes cause it to pick up radiated hum from other equipement. Suspect this if the hum changes loudness or tone when you move or turn the amp. There is usually nothing you can do about this except move the amp to where the hum is less.

Poor internal wire routing

If the signal leads inside the amp are routed too near the AC power wires or transformer, or alongside the high-current filament supply wires, they can hum. Sometimes using shielded cable for signal runs inside the cabinet can help. It is hazardous to do, but you can open the amp up and use a wooden stick (NOT A PENCIL) to move the wires around inside to see if the hum changes. This is hard to do well and conclusively, since the amp will hum more just because it is open. BE VERY CAREFUL NOT TO SHORT THINGS INSIDE THE AMP.

Poor AC Chassis Ground at Power Transformer

A common problem is the main ground point to the chassis. The green wire (you DO have a three wire line cord, don't you?) ground to the chassis, the "line reverse" cap, the CT on the filament windings, the CT on the high voltage windings, and other things associated with power or RF shield grounding are often tied to lugs held under one of the power transformer mounting bolts. If this bolt becomes loose, or if there is corrosion or dirt under the lugs, you can get an assortment of hum problems.

Defective internal grounding

There are potentially lots of places that must be tied to ground in the internal wiring. This varies a lot from amp to amp. If one is broken loose or has a poor solder joint or poor mechanical connection, it can show up as hum. Note that modified amplifiers are particularly susceptible to this problem, as the grounding scheme that the manufacturer came up with may well have been modified, sometimes unintentionally. With the amp unplugged, open and the filter capacitors drained, carefully examine the wires for signs of breakage or mods.

Relay Coil Hum

If your amp is home-built, you may have used an AC-coil relay for some switching functions. If you used the filament AC for powering this relay, you can get an AC hum in the signal path induced from the coil. The cure is to run this relay from DC by rectifying and filtering the filament supply or changing to another type of relay that's less susceptible to causing hum. Of course, for homebuilt amps, there could be many hum-inducing problems.