The Valve Wizard

Fuses are a necessary element of power supply design. They serve to protect both the user and the amplifier itself- particularly the transformers. They also provide a useful first port-of-call if anything goes wrong, as the fuse which has blown can give an indication of where in the circuit the problem occurred.

The fuse value used is often fairly vague- they are not precision devices, but where possible they should be of the minimum current value possible, for best circuit protection. Occasionally the inrush current on switch-on will be large enough to blow a fuse so a slightly larger one will be needed. It is usual to build the amp, use the smallest value you think will work and see if the inrush is too much. If it is, try progressively larger values until the right one is found.
A thermistor could also be used to limit switch-on surge current.

Most designs require only two fuses: One on the mains supply to protect against heavy surges both to and from the power transformer, and one in the HT supply to protect the power and output transformers from failure within the amplifier. They don't provide a great deal of protection for other components, including valves, as the response time of a fuse is too slow to save them before the damage is done, but they are better than nothing.
Thankfully, transformers can survive an overload long enough for a fuse to blow, and most valves are not as fragile as some would have you believe. Most other components in the amp are cheap and easily replaceable and not such a painful loss. The most fragile components are the sorts of things that have to be replaced (fairly) often anyway (e.g. smoothing capacitors and valves), unlike the transformers, which are the most valuable part of the amp and should be our primary concern.

The HT and mains fuses are usually accessible via panel-mounted fuse holders at the back of the amp. The best way to wire these is to connect the live (hot) wire to the tip connection. That way it can never come in contact with a live voltage from the side connector as you remove it from the holder.
The two main types of fuse are glass or ceramic, available in 20 x 5mm and 32 x 6.3mm sizes. Fuses used on the mains must always be of the ceramic type (these are and-filled to prevent the fuse wire vapourising onto the surface of the tube and leaving a conductive path even after the fuse has blown). Fuses on the secondary side of any transformers, and within the amp circuit proper, are normally of the glass type.
Although fuses are normally rated for AC mains voltages this is not normally a concern, even though we may place it in a DC circuit at much higher or much lower voltages. It is the current which causes a fuse to fail (by melting the fuse wire) while the voltage has very little influence. It is therefore perfectly usual to use mains voltage fuses at other voltages (assuming you are not dealing with voltages in the kilo-volt range!)

Plug fuses: The fuses used in mains plugs (if you live in a country sensible enough to have them) should normally be rated at 5A or less for a normal amp. 1A is the lowest value commonly available, and this is usually sufficient for amps smaller than 60W.
A plug fuse is a necessity for any electrical appliance, all amps should have a mains fuse AS WELL as a plug fuse.

Fuses in amplifiers: The usual type of fuses used in amps are 'anti-surge', also known as time-delay or slow-blow (Slo-Blo US), and are commonly available in values as low as 50mA. They will not blow during a brief current overload (less than a couple of seconds), but will blow in the event of a prolonged surge. In circuit diagrams they are often given the symbol 'T'.

Mains fuse: The mains fuse should be placed in series with the LIVE wire (brown in the UK). Ideally it should also be placed before the power switch, so it will usually be the very first thing in the circuit, where the mains comes into the amp. Some appliances use two fuses, one for live and one for neutral. While there is some argument against using a neutral fuse, there is no law against it (in the UK anyway). You can buy IEC inlet sockets with built-in fuse holders, which greatly simplifies construction.
The fuse value used depends on the current draw of the amp. Most amps use a 1A mains fuse- a power transformer primary winding should be able to handle a 1A surge for several seconds quite easily.
Larger amps (e.g., more than 60W) may have such a large current draw under normal conditions (especially the switch-on surge) that a 2A or 3A fuse will be necessary.
Remember, the HT usually has its own fuse but the heater and bias supplies usually don't, so a failure in one of those is only protected by the mains fuse.

The HT fuse: You will see the HT fuse in different positions in existing amp designs, and some are better than others:

Immediately after the rectifier (not recommended): This will protect everything after the rectifier, but will not protect the power transformer against a rectifier short circuit (which is one of the most common failure modes when using a silicon rectifier!). This may not be such a problem when using a valve rectifier as shorts are much less likely. However, it has been argued that normal AC fuses will not blow at the expected moment when used in a DC circuit.

In series with the transformer centre tap or bridge rectifier ground connection. Although this will technically turn everything 'off' in the event of a failure, the HT will still be at a high potential because the rectifier is still connected to the power transformer in the normal way, so although current has ceased to flow, it has not made the amp as safe as it could be for the untrained amp tech...

Before the rectifier, in series with the power transformer HT secondary (recommended): This is the best place for the HT fuse as it protects everything, and is also in the AC part of the circuit where most fuses are designed to work.
With hand-wired amps this is perhaps less practical with a two-phase rectifier since it requires two fuses, one for each leg of the transformer secondary.

Some amp designs also place a fuse at the centre tap of the output transformer, or in the cathode circuit of the power valves purely to protect the transformer and power valves. This is not absolutely necessary, but is an extra bit of 'cheap insurance' for the valuable output transformer!

Heater and fixed bias supplies: Heater supplies are not normally fused, partly because heater supplies are usually very simple so very little is likely to go wrong, and partly because they supply high currents. This means that the difference between normal operation (which could be as much as 7A in a 100W amp!) and a short circuit (failure) could be quite small, making a fuse of little use since it would need to be a heavy fuse to withstand the inrush current at start up. Nevertheless, heater fuses are becoming more common in commercial PCB designs.

Fixed bias supplies must not be fused. If a bias supply were shut off by a fuse while the amp was running it would leave the power valves under-biased, probably leading to their immediate destruction, and possibly taking the output transformer with them. Since bias supplies are usually very simple there should be no need for a fuse anyway in a well built amp. In the unlikely event of a serious failure in the heater or bias supply, they are still protected by the mains fuse. Admittedly it may take some time to blow, but it will at least turn off the whole amp. In more critical designs we would probably devise some sort of active bias-monitoring circuit which would shut down the whole amp, rather than just rely on the mains fuse.