I want to test the voltage drop of a conductor as the conductor increases in length, at 120V. I do not have a 120V bench power supply. Is there a safe way to connect the electricity from my wall outlet (that runs at 120V AC) to a set of probes/crocodile clips that I can attach to the conductor?
I believe what you are going to want will be an isolation transformer. This will protect you by not referencing the power supply from the transformer to earth ground and you will not shock your self by touching one of the conductors, as you will not become the ground path (you are earthed and the circuit is not). However, this will not protect you in the event that you short the conductors (touch them both at the same time). It is safer than connecting to mains power directly, but not completely safe. Never tell yourself that electricity is completely safe.
The safety of any power source is indicated by current flowing through the circuit in to the source. Small sources have pre-defined current sourcing\ sinking capability but since you are using power outlet directly this part should be fine.
Now if you want to measure the conduction\ resistance behavior of conductor at a specified voltage you'll have to think of something that will bring the current flowing through the conductor to a safe value (may be use a rheostat).
I don't think connecting the set of probes/crocodile clips directly from outlet is good idea as it will definitely cause short circuit.
BTW you can directly know the voltage drop with increase in length if you know the material property of the wire with the equation R = ρ*L/A.
But if you are doing it to get some practical data, please do not connect it directly until you have some sort of current protection in your circuit.