What is a one-bit ADC good for?
To give a basic example of how a 1-bit ADC can be used to obtain useful information from a waveform, take a look at this circuit. It uses a triangle wave to turn the information into a pulse width modulated output. This is a similar but simplified version of how other 1-bit ADC techniques work, by using a (usually fedback) reference signal to compare the input to.

Circuit



Simulation



Magnified Timescale View:



We can see from the top input waveform, the triangle wave is used to compare the waveform at different points through it's period. As long as the triangle wave is of a considerably higher frequency than the input (the higher the frequency the more accurate), this causes the comparator to output an average of high/low depending on the voltage level of the waveform.
To see how we can reproduce the original waveform from the PWM data, the comparator output is fed into a low pass filter, and out pops the sine wave again.  

For further reading:

Delta-Sigma Converters
Successive Approximation ADC
Single Bit ADCs
Ramp Compare ADC (Counter ADC)