I'm doing a sound-maker project that will have several volume controls. Does it make any difference if I wire each potentiometer using only two terminals (as a variable resistor) or is there an advantage to using all 3 terminals? (voltage divider/potentiometer) . Somewhere long ago I read that having the third terminal connected to ground has some benefit.

 

You have answered your own question.
A two-terminal potentiometer is a variable resistor.
A three-terminal potentiometer is a voltage divider.
There is a huge difference between the two.

 

What do you mean by "several" volume controls?

 

My project involves having eight 555 timers, each one making a different audio tone, triggered in sequence by a 4017 sequencer. I will need a lot of potentiometers to control the volume and frequency of each audio 555, the frequency of the 'clock' 555 that sends pulses to the 4017, as well as a master volume knob.

In the past, every time I needed to control volume or signal level in a circuit, I used a potentiometer wired using only 2 terminals (middle and one of the outer ones) and it worked fine. Is this the correct way to control volume/level?

 

If the pot is part of a gain control circuit, like the series feedback resistor in an opamp circuit, then it can function with only two connections as a variable resistor. If it is a true volume control, a variable attenuator that can take it's input signal all the say down to zero, then you need all three connections. Post a schematic of your previous connection ways and we'll comment.

ak