An additional caveat... sometimes you actually want randomness.
In cryptographic (security/authenticity) applications, pure "unguessable" randomness is required. Using a converter's LSB's (those below noise floor) is a quick way to generate purely random numbers.
When the ADC hardware is available for other purposes (sensors and the like), it's a quick-and-easy way to seed secure communication. You can enhance the effect by maximizing the gain on the input amplifier if available (many MCU's offer such a feature) and floating the input.
ADC randomness primarily derives from two physical principals: quantization-noise and thermal noise.
These effects have a threshold at the macroscopic level. For example, numbers sufficiently away from the bit boundary don't need to be rounded and therefore experience no quantization error or randomness. Thermal noise doesn't affect the more significant bits in the conversion in most scenarios.
By extension, you can see that varying the conversion parameters (sampling time, depth, rate, reference voltage) will effect change in the randomness of the results by moving the threshold of randomness (either increasing it by raising or decrease it by lowering the threshold). Similar effect is accomplished by varying the environmental/system parameters (temperature, power supply, etc).
That said, many successful commercial hardware random number generators rely on this technique because outside effects, only reduce the randomness -- they by no means eliminate it (physically impossible).
You can compensate for a reduction in randomness by doing more conversions and appending the results. This process of bit-extension (concatenation of successive conversions' low-bits) is used in the STM32 Nucleo Dongles, the FST-01 (including NeuG 1.0), LE Tech's Grang family of devices, and many others.
The Grang devices generate bits by converting at over 400 million conversions per second (1 bit per conversion). If you do enough conversions you can guarantee high randomness even in the face of environmental conditions.