When you power up a Prius, it goes through a very different sequence than a normal gas-only car. First, it uses its auxiliary 12V battery to bootstrap its electronic systems. Then, when the computers verify that everything is OK, they switch on the high-voltage battery that then powers the car and recharges the 12V battery as needed. If the car later needs to start its gas engine, it uses a motor-generator driven by the high-voltage battery to start it more quickly and with less engine stress than a 12V battery could manage.
This has led to some discussion about how much power is required from the 12V battery to get the car started – it seems like it would be much less than is needed to crank over the engine in a conventional car, but how much less? And, as a practical matter, how small a battery pack would you need to jump-start a Prius with a dead 12V battery?
To help answer these questions, I measured the current drawn by my 2005 Prius during several startup sequences and captured the current profiles for analysis. To be technical, the waveforms shown below were captured using a Fluke Y8100 AC/DC current probe clamped around the ground wire of the 12V battery and connected to a Tektronix TDS210 digital storage oscilloscope. My car is a 2005 Prius with the BC option package (i.e. fully loaded), and these measurements were taken with the passenger's door and rear hatch open, all dome lights turned off, and smart entry disabled.
The startup sequences all seemed to have one of two profiles. Here is the simplest one:

This shows current on the vertical axis, with each major division being 5 amps, and time on the horizontal axis, with each major division being 1 second. The "1>" symbol at the lower left indicates the zero-current line; I meant for it to correspond with the lowest major division but missed slightly when I was setting up the scope.
The car began by drawing about 2 amps for a little over 2 seconds, until I pressed the brake pedal and the current jumped to about 6 amps. Several seconds later I hit the Power button, and the current did an elaborate dance between 15 and 30 amps for several seconds, and then abruptly went negative as the hybrid system kicked in and began to recharge the 12V battery.
That was the most common startup profile, but occasionally I managed to get one that looked like this:

When I pressed the brake pedal this time, the car drew about 15 amps for almost three seconds as it ran the electric brake-pressure pump before settling down and doing a startup profile like the one above. In an emergency jumpstart you could pull the brake-pump fuse before starting to eliminate this energy draw. (Just be sure to replace the fuse before you drive off!)
The peak current in both of the waveforms above appears to be about 30 amps, but one startup showed a much higher peak:

Note that the vertical scale here is 10 amps per major division, which makes the peak current nearly 60 amps. This profile seems to be in between the two shown above, with a high-current step like the second one above, but much shorter. Again, this could probably be eliminated by pulling the brake-pump fuse.
My oscilloscope unfortunately won't integrate the area under a curve, but if I do an eyeball integration on the middle waveform I get only about 90 amp-seconds (even including pressurizing the brake system). This is a tiny amount of energy, so tiny that one could imagine jump-starting a dead Prius with a stack of six or seven AA batteries if one didn't think too hard about the 30-amp current peaks required. (I've seen internal resistances of 0.1 to 0.15 ohms quoted for alkaline batteries, which would limit the peak current to much less than that.)
I have heard from one person who indeed tried to start a 2001 Prius with a stack of D-cell batteries, and then a pair of lantern batteries, without success but was able to start it with a 7 amp-hour gel-cell battery. He had heard someone else claim that a 1.8 AH gel-cell would work but couldn't personally confirm it. Both of these clearly contain orders of magnitude more energy than is required (as do the lantern batteries, for that matter), so I suspect the limiting factor is the ability to briefly supply 30 amps without too much voltage drop.
For what it's worth, here's a picture of the business end of my measuring setup:

It's a little hard to see, but the jaws of the current probe are clamped around the wire that goes from the negative terminal of the battery to ground. And here's the other end of the setup:

I think the laptop and the scope are feeling a little abashed here; it's the first time either of them have been in a car that has more computing power than they do!