The equipment I have needs +5V +12V and -12V supplied to it. The old PSU which provided all the voltages blew to bits. I have sourced a PSU1 +5V (30A), and PSU2 &PSU3 (two identical +12V (2A) stand alone supplies). Am I right in thinking if I link the 0V from PSU1 to 0V PSU2 and +12V of PSU3 I will achieve my +5V, +12V and -12V (from the 0V of PSU3)? Or is it not that simple and I can expect a bang?
If your three power supplies are isolated from their input, which is most likely the case if they are line powered, then what you propose should work fine.
A isolated power supply produces a voltage difference not some absolute voltage. This voltage difference is usually talked about with the assumption that the negative side will be considered the 0 V reference. This simplifies descriptions and calculations, and is often exactly what will be done with the supply. However, there is no rule that says the negative output must be connected to what the rest of the system considers 0 V.
Note that this can only go so far. There should be a spec as to what the maximum isolation voltage for the supply is. This says how far the output can float relative to the input. That might be 1000 V, for example, for a line-powered supply. If you put more than that between output and input, the result could be pyrotechnics.
Again, the above is all assuming this is a isolated supply. Most line-powered supplies are isolated. If it only has a two-prong plug, then it should be isolated. Some bench supplies have three output terminals, the floating differential output and the line ground brought out to a terminal. These usually have a optional grounding strap you can connect between the ground terminal or either output, or leave disconnected to let the output float.
What your are suggesting can work, but only if the PSU's outputs are isolated from the AC ground and neutral!
Once you get the PSU's, do a few continuity checks with a multimeter. With the PSU unplugged, there should be no connection between the DC COM (DC-, 0V, etc) terminal to either the GND or N lines of the incoming AC.