I rambled on quite a bit here. Please forgive the detailed coverage of the basics if you already know this stuff. I include them for the use of any others who might stumble on this. If I make any mistakes along the way, someone bust my chops on it. This is safety stuff after all.
Yep, that is what I am concerned about and fuses seems like the simplest solution. I have never added fuses to anything I have designed before, is there anything special I should know about?
It is important to choose a fuse that will blow before
any connection between the power supply board and your load becomes a fuse itself. Have a look at the power supply mainboard connections for the output wires. In most that I have seen there are several wires for each high current supply voltage (+5V, +12V, and likely +3.3V) and an enormous amount of ground wires. The reason for all this redundancy is that each wire is expected to share a portion of the maximum rated load. If any single wire is forced to conduct a large portion of the load alone it will very likely heat up, smoke off it's insulation, and turn into a light bulb filament, or just vaporize with a bang. If the wires are marked you should be able to calculate the safe load each can conduct alone with a little internet searching. Remember that the ground is sinking the current from all the positive supplies that are drawing load, and that accounts for the larger number of wires (or thicker wires/traces) that are present on the ground side.
This means that you cannot, for example, just drop one of the +5V wires to your output and then draw 10A through it without damaging that poor lone wire, and if this should happen
you should open the supply back up and verify that nothing was damaged. It might seem to work fine, but you want to be sure that the wire insulation isn't compromised and the connections are still good. I've seen a wire melt off it's insulation in tiny spots everywhere it was under stress, which turned out to be the outside curve of all the bends it made. The supply worked fine, but would have been very dangerous to operate with all that naked wire inside. If the wire looks at all odd, replace it.
The solution is to determine the safe capacity of a single wire and use as many in parallel as you need when connecting them to your output terminal. This goes for the ground connection too, and even more so if you plan on using multiple voltages at the same time. You may notice that the supply can produce -5V and -12V with respect to ground at very small currents, usually less than one amp. These wires will likely be single leads from the board because the supply will current limit them before the wire itself is in danger.
The last bit to be sure of are your output terminals. Make sure you have good solder connections, and if you use screw terminals make sure the resistance through them is low. I've had screw terminals heat up quite a bit because of a loose connection. If your terminal (or any part of the circuit really) feels warm under a normal load then you've found a weak spot that could use shoring up.
That covers the inside of the supply, now for the outside. Every part of the circuit counts when a high current is drawn. Whatever you use to connect your supply to your project, hookup wire on a breadboard, wire connection to the breadboard buss, and the breadboard buss itself. For example, a cheap breadboard will probably start to have problems at about one amp, but I haven't seen ratings listed for many of them.
The short version to all this is that you should be as certain as you can that everything from the solder connection of the wires to the power supply board all the way to your project and back again is capable of handling the max current the supply can produce. Adding a fuse reduces the effective max current capacity, but you have to be aware of what else is in the circuit and ensure that the fuse is the weakest link. If the weakest link is not the fuse, you may be in store for heat, smoke, and fire.
I ran on about this ad nauseam because I think the frame of mind is more important than a simple answer. My apologies if it was a bit excessive.

Keep in mind as well that you can use more than one method for current protection. You can use an inline fuse in your power supply to protect your wiring, and a separate fuse on your breadboard input to protect the buss strips. You can try other forms of current protection too, like breakers and
polyswitches (which are likely already present in the power supply elsewhere), just be aware of their limitations and cost.
From what I have read, most people suggest a 10W 10 Ohm resistor on the 5V line.
I was blessed with several older AT power supplies which switch on with a mains voltage loaded toggle (!). I solved this by bypassing the toggle internally and turning the supply on and off with an old power strip that has a toggle for each output, the old sort you used to see under the monitor of old computers with a switch for the computer, monitor, printer, etc. all separate. Some of the ATX power supplies do require a load as you suggest, but you may find yours doesn't. Some have reported success simply using a LED and matched resistor as an indicator light, which draws a great deal less current and produces less heat. I don't have a good answer for you, but you can apply the same methods to be sure that whatever solution you come up with doesn't contain a dangerously weak conductor.
All told, this is a great way to get a cheap bench supply and learn about power delivery. I'm still using the old AT supply that once powered my first IBM clone to power my new projects, and that's satisfying. Just be sure to avoid electrocution, fire, and that sort of thing.
Hope this helps some.
