Is there a secure source of entropy on a typical microcontroller? On a device that does not have a hardware RNG, what is the best source for entropy? 

Some options and pitfalls floating around: 


Use the ADC to read something analog: can become deterministic if there is access to power supply or some ADCs are just too stable even at LSB.
Use un-init SRAM: power supply brownout attack?
Use crystal jitter:  idea here is to sample the variance between the RTC and MCU crystals and use LSB.
Most microcontrollers that are suitable for crypto I've seen have a variant with a hardware RNG. For example the PIC32 series by Microchip. 

However, if not, what you could do is attaching some sensor to an ADC. It would depend on your environment what kind of sensor you could use. It can be anything, which is not easily manipulated (at least not in the LSB(s)).

Then, take the LSB(s) from the ADC, or better yet, use a randomness extractor. How often you can fetch me bits, and how many you can fetch at a time, depends on the ADC, the sensor and the environment, and the security level you want to reach. 

If you can go a bit further than just your microcontroller, there are some small hardware circuits that can be used to create randomness. One example is using a diode's avalanche effect.


  Avalanche noise is the noise produced when a junction diode is operated at the onset of avalanche breakdown. It occurs when carriers acquire enough kinetic energy under the influence of the strong electric field to create additional electron-hole pairs by colliding with the atoms in the crystal lattice. If this process happens to spill over into an avalanche effect, random noise spikes may be observed.


In short, we can use a diode with some external circuitry to create random noise spikes. If we then amplify that signal and feed it to a comparator, we get a random bit string.