Can I tie all the negative leads from multiple power supplies together and call it ground?
I wonder because I have 24V power supply, a 12V power supply and a 5V supply involved in a project.
Is it safe to tie the negatives of all these supplies together and call it ground?
Probably. But depending upon how much current flows through the wires, there may be voltage imbalances. For example, if you push 10A of current through a long wire of 0.1 ohm resistance, that's a 1V difference from one end of the wire to the other. Kinda blows away the whole "this is ground" idea.
But if you are working with low currents then you can probably just tie all the supply negatives together and call it "ground".
Besides, if you're young, just try it and see what happens 
If you're old, study the problem carefully, design a star-ground arrangement carefully, THEN try it and see what happens.
Yes, it's generally a good idea to do that, especially if you have components powered from the different sources that communicate with each other or are otherwise tied together.
Is it safe to tie the negatives of all these supplies together and call it ground?
It is required in many cases to do just that and also remember to tie this common ground to an Arduino ground pin. Just try and make sure the large current loads (motors, relays, solenoids, etc) have their own wires going to both the + and - terminals of each power supply that powers them, the new common wire should be a seperate wire(s). This should help large current spikes from being seen by the other voltage loads, called 'ground bounce' by some.
Lefty
It should defnitelly work as everyone says for small currents. Just try to keep everything close together, use a star type topology and have separate ground paths for high powered loads.
The problem of ground loops that can creep up which results in your "ground" being at different potentials at different points can wreak havoc signals.
Also make sure you properly connect everything together and get the lowest possible resistance between all ground points.
I have done something like this and I was having hair pulling frustration only to discover one of grounds was floating and not connected because of a badly crimped terminal. :-[
As for current, the lamps are going to be pushing 12 Amps off a 24V supply and the arduino is going to be running off a 24VDC to 12VDC converter along with a few 120mm fans. The 5V supply pin on the arduino is going to be supplying about 150mw at 5V to a dimming circuit for the lamps.
I'll google "star ground configuration" and see if I can learn anything about that.
Perhaps post a big-picture block-diagram view of what is connected where and we can point out your trouble spots. The 12A lamps and fans could get you in trouble.
The block diagram is below, the little circles represent ground.
There is a 24V power supply. I'm building 3 LED lamp fixtures, each of which will contains 24 high power LED's and will consume about 4 Amps at 24 Volts. The first module connects to the second one, and the second one to the third one.
The rest of the system runs off a 24V to 12V DC to DC power supply. The arduino runs off this voltage. Also, each module has a 120mm computer type cooling fan that runs off 12V.
The arduino's 5V supply is used to run a dimming circuit that controls a dimming pin on the constant current supplies in the LED fixtures. This dimming circuit will consume about 150mw to control the LED drivers.
The power supplies and microcontroller are going to be about 4 feet from the lamps. The lamps are going to be about 1 foot from each other and are one foot wide, for a total run from the power supply to the last lamp of about 8'.
In your block drawing, I would run three ground wires and use the 24vdc ground as the common 'star ground'. So one wire from the lamp module string ground to the 24vdc negative, one wire from the 12vdc supply ground to the 24vdc supply ground, and one wire from the 24vdc ground to the Arduino's ground.
Lefty