Electronic – arduino – Beyond board power, understanding multiple power supplies and loads in a circuit

You really haven't given us any actual information to help you with other than you don't want an Arduino shield solution. What kind of power supply do you need? How many voltages, and at what current levels? Are you just powering the AVR? Do you need galvanic isolation?

I have successfully used National's LM5071 PoE PD controller in one of my designs. Depending on how you want to hook it up, it'll give you full galvanic isolation and multiple output voltages. My particular setup gives me 3.3V at 2A and a separately-isolated 5V at 1A. I "slave" an LTC3523 off the 3.3V to give me 1.8V and 5V supplies that aren't isolated from the main 3.3V supply.

Many companies offer PoE PD controllers. National, Maxim, Linear Tech, TI... Have you done any poking through their websites to see what's out there so you can narrow down your search?

EDIT now that I have more information from the edited question. :-)

TI's TPS2370 looks like a perfect fit. It's an 8-pin SOIC device that takes care of the 802.3af spec part and you can drive pretty much ANY regulator off of that. So a really simple supply would consist of the TPS2370 and something like the BD9001 (personally I like Linear's LT1676 but I don't think it has a high enough input voltage spec for PoE) from the previous answer. Two 8 pin SOIC devices, a handful of passives and a small inductor would get you what you're after.

A constant power load varies it's impedance on change of input voltage to keep the power constant. A constant impedance load is simply a load that presents an unchanging impedance, like a resistor. An L-Pad is used to change speaker output level whilst maintaining a constant impedance load to the amplifier.

A good example of a constant power load is a switching regulator. Since this has to maintain it's power into it's load, it must draw the same power from it's source even if the source changes voltage.
This is also an example of a negative impedance because in order to maintain the output power, if the voltage in drops, the current must rise (opposite to a standard resistor where the current and voltage rise/fall with each other)

Here is an example circuit, made from a LT1377 boost switching regulator:

Here is the simulation:

The input voltage V(in) (blue trace) starts off at 4V, and gradually rises up to 10V. We can see the power (red trace) stays constant at ~1W over a change of 6V at the input (it's not perfect as it's meant to represent "real life" and not 100% efficient, but it's pretty close)
We can also see the dynamic negative resistance characteristic (green trace) which is due to the input current falling as the voltage rises. Tt falls from ~300mA to ~120mA over the voltage rise from 4V to 10V - don't be confused by the minus sign, that's just the direction of measurement in LTSpice.
The dynamic resistance slope can be roughly calculated by (4V - 10V) / (300mA - 120mA) = -33.3Ω. Looking it another way, 6V / -33.3Ω = -180mA.