Submitting for Ye Olde blocking oscillator ("joule thief").
It works down to whatever Vbe is (so, ~0.7V for Si, less if you're willing to allow vintage Ge), and startup can be had from a JFET or depletion MOS oscillator which can start up as low as the 10s mV.
(There are SiGe RF transistors, but the Ge is employed in the B-C junction IIRC, greatly enhancing performance, but not affecting Vbe much compared to Si.)
A relevant property of the blocking oscillator is, when gain is adequately high, it can kick on with very little bias indeed, and then do a single cycle, or burst of cycles, depending on the values of base resistance and capacitance. When the time between bursts is quite long, well, it visibly flashes.
I once made a reasonably-scaled joule thief, that is, capable of about a watt into an illumination grade LED:
Of course you'll notice that's a 1.5V cell (or 1.2V, I most often have a NiMH in it), so it's doing the business. It's more of a flashlight than a flasher, but I'll get to that in a moment.
That's a 3A low-Vce(sat) transistor (such as PBSS303NX), which boasts quite excellent hFE and Vce(sat), even up to quite high currents. And, so it seems, down to low currents as well. The switch selects between open, 1k and 100R for the base bias, giving "off", low and high power settings. If I touch my finger across the switch terminals while in the "off" position, I can make it blink at some fractional Hz as my skin leakage (~Mohm) charges the base bypass cap, which eventually kicks over and fires off one pulse. And being the pulse is a few watts, it's quite brightly visible despite being only some microseconds in duration.
I think you'll have a hard time going lower (in voltage) with a charge pump architecture, but inductors are fine down to whatever. Eventually the problem is getting enough power at all; you need very thick semiconductors indeed to obtain any kind of useful power from a handful of thermocouples, say (~10s mV, so even 100mW needs some ~A!). The advantage of a charge pump is, it doesn't need to switch fast, just solidly enough to not lose a bunch of charge in the process.
Another difficulty is the "valves" in the "pump" -- doing it the easy way, with diodes, loses you a ton of Vf. (Consider the losses in a voltage multiplier or Cockroft-Walton stack.) This is another case where integrated circuits shine; it's no problem to load up a couple dozen CMOS switches, complete with level shifting driver circuitry. Have fun doing all that on the breadboard (where you can't even get 4-terminal MOSFETs, except for a very few outliers).
Tim
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