I'm messing around with diodes right now. The behavior is strange.
Some circuits I breadboarded:

Circuit 1
Expected: All of V_Source is dropped across the diode D1. If V_Source is greater than D1's forward voltage, current flows. The relationship between voltage and current is non linear, so Ohm's law doesn't hold.
Actual: If V_Source is greater than D1's forward voltage, the voltage across D1 is always the forward voltage. It'll draw as much current as it can to keep the voltage across it equal to the forward voltage. Good thing I had OCP turned on.
Circuit 2
Expected: V_Source minus D2's forward voltage is dropped across R1. R1 effectively "linearizes" the circuit once D2's forward voltage is exceeded. Circuit current will be equal to (V_Source - D2_FV)/R1.
Actual: Worked as expected. Some variation of the diodes forward voltage depending on the paired resistance value. Lower resistance/higher current increased forward voltage. Is this just movement along the diode's V/I curve?
Circuit 3
Expected: Similar to circuit 2. R2 and R3 will divide V_Source less D3's forward voltage.
Actual: Mostly worked as expected. I played around with the ratio of the resistors and found some odd behavior. Diodes are "greedy". If R3 is 500K and R2 is 100R pretty much all of V_Source should be dropped across R3. There shouldn't be enough voltage left to get the diode to work. But there is a voltage drop across the diode and it's conducting.
I experimented further with circuit 3 and mapped the total circuit voltage vs total circuit current. It's way more linear than I thought it would be. I almost wonder if these diodes are bad or something. But I checked them with my DMM and it shows a forward voltage around 550mV. It's just weird that I don't see that in the circuit.
Here's the excel file with the graph:
https://dl.dropboxusercontent.com/u/91808950/Diode%20V%20vs%20I.xlsx